G. Alefeld and J. Herzberger, Introduction to Interval Computations (Academic Press, New York, 1983) 67--119.
G. Alefeld, Existence of solutions and iterations for nonlinear equations, in: R.E. Moore, Ed., Reliability in Computing: The Role of Interval Methods in Scientific Computing (Academic Press, New York, 1988).
G. Alefeld and F. Potra, On two higher order enclosing methods of J.W. Schmidt, Z. Angew. Math. Mech. 68 (1988) 331--337.
G. Alefeld, On the convergence of some interval-arithmetic modifications of Newton's method, in: R. Steplemen et al., Eds., Scientific Computing (North-Holland, Amsterdam, 1983) 223--230.
G. Alefeld, Eine Modifikation des Newtonverfahrens zur Bestimmung der reellen Nullstellen einer reellen Function, Z. Angew. Math. Mech. 50 (1970) T32--T33.
G. Alefeld, On the order of convergence of the interval-Newton method, Computing 39 (1987) 363--369 (in German).
G. Alefeld, Uber das Divergenzverhalten des Intervall-Newton-Verfahrens, Computing 46 (1991) 289--294.
G. Alefeld, Bounding the slope of polynomial operators and some applications, Computing 26 (1981) 227--237.
G. Alefeld, Stets konvergente Verfahren höherer Ordnung zur Berechnung von reellen Nullstellen, Computing 13 (1974) 55--65.
M. Altman, Iterative methods of higher order, Bull. Acad. Pol. Sci. Ser. Sci. Math. Astr. Phys. 9 (1961) 63--68.
D. Anbar, A stochastic Newton--Raphson method, J. Stat. Planning Inference 2 (2) (1978) 153--163.
M. Andrews, S.F.McCormick and G.D. Taylor, Evaluation of functions on micro-processors: Square root, Comput. Math. Appl. 4 (1978) 359--367.
J.W. Archbold, Algebra (Pitman, London, 3rd ed., 1964) 122--133; 174--207.
B.W. Arden and K.N. Astill, Numerical Algorithms: Origins and Applications (Addison-Wesley, Reading, MA, 1970) 54--80.
D.W. Arthur, The use of interval arithmetic to bound the zeros of real polynomials, J. Inst. Math. Appl. 10 (1972) 231--237.
K. Atkinson, An Introduction to Numerical Analysis (Wiley, New York, 1978) 39--106.
V.A. Bailey, The solution of algebraic equations by means of tables of logarithms, Philos. Mag. Ser. 7 18 (1934) 529--539.
M. Balfour and A.J. McTernan, The Numerical Solution of Equations (Heinemann, London, 1st ed., 1967).
J.P. Ballantine, Complex roots of real polynomials, Amer. Math. Monthly 66 (1959) 411--414.
E.J. Barbeau, Polynomials (Springer, New York, 1989).
E.H. Bareiss, The numerical solution of polynomial equations and the resultant procedures, in: A. Ralston and H.S. Wilf, Eds., Mathematical Methods for Digital Computers, Vol. 2 (Wiley, New York, 1967) 185--214.
B. Barna, Über das Newtonsche Verfahren zur Annäherung von Wurzeln algebraischer Gleichungen, Publ. Math. Debrecen 2 (1951) 50--63.
B. Barna, Über die Divergenzpunkte des Newtonschen Verfahrens zur Bestimmung von Wurzeln algebraischer Gleichunger, I, Publ. Math. Debrecen 3 (1953) 109--118; II, ibid. 4 (1956) 384--397; III, ibid. 8 (1961) 193--207; IV, ibid. 14 (1967) 91--97.
S. Barnard and J.M. Child, Higher Algebra (Macmillan, New York, 1936) 81--105; 179--199; 446--466.
W. Barth, An algorithm for the computation of all real zeros in an interval, Computing 9 (1972) 327--333.
W. Barth, Nullstellenbestimmung mit der Intervallrechnung, Computing 8 (1971) 320--328.
M. Bauer, Zur Bestimmung der reellen Wurzeln einer algebraischen Gleichung durch Iteration, Jahresber. Deutsch. Math.-Verein. 25 (1917) 294--301.
F. Bauhuber, Direkte Verfahren zur Berechnung zur Nullstellen von Polynomen, Computing 5 (1970) 97--118.
H. Benzinger, S. Burns and J. Palmore, Chaotic complex dynamics and Newton's method, Phys. Lett. A 119 (1987) 441--445.
I.S. Berezin and N.P. Zhidkov, Computing Methods, Vol. 2 (Pergamon Press, Oxford, 1965) Chapter 7.
W.A. Beyer, A note on starting the Newton--Raphson method, Comm. ACM 7 (1964) 442.
Z. Bi and P.H. Calamai, A class of root-finding methods, BIT 29 (1989) 458--463.
A. Björck and G. Dahlquist, Numerical Methods (Prentice-Hall, Englewood Cliffs, NJ, 1974).
E. Bodewig, Konvergenztypen und das Verhalten von Approximationen in der Nähe einer mehrfachen Wurzel einer Gleichung, Z. Angew. Math. Mech. 29 (1949) 44--51.
W.F. Bodmer, A method of evaluating the complex zeros of polynomials using polar coordinates, Proc. Cambridge Philos. Soc. 58 (1962) 52--60.
A.D. Booth, Numerical Methods (Butterworth, London, 1955).
S. Borofsky, Elementary Theory of Equations (Macmillan, New York, 1950).
C.A. Boyer, A History of Mathematics (Wiley, New York, 1968).
D. Braess, On the regions of attraction when computing the roots of polynomials with the Newton-method, Numer. Math. 29 (1977) 123--132.
R.P. Brent, Multiple-precision zero-finding methods and the complexity of elementary function evaluation, in: J.F. Traub, Ed., Analytic Computational Complexity (Academic Press, New York, 1976) 151--176.
R.P. Brent, Some high-order zero-finding methods using almost orthogonal polynomials, J. Austral. Math. Soc. Ser. B 1 (1975) 1--29.
R.P. Brent, A class of optimal order zero-finding methods using derivative evaluations, in: J.F. Traub, Ed., Analytic Computational Complexity (Academic Press, New York, 1976) 59--73.
S. Breuer and G. Zwas, Polynomial iterations for root extraction, Comp. Educ. 12 (1988) 289--300.
P.A. Brooker, The solution of algebraic equations on the Edsac, Proc. Cambridge Philos. Soc. 48 (1952) 255--270.
L.E.J. Brouwer and B. de Loor, Intuitionistischer Beweis des Fundamentalsatzes der Algebra, Nederl. Akad. Wetensch. Proc. 27 (1924) 186--188.
R.A. Buckingham, Numerical Methods (Pitman, London, 1957) 251--304.
S. Burgstahler, An algorithm for solving polynomial equations, Amer. Math. Monthly 93 (1986) 421--430.
J.-C. Yakoubsohn, Sur un procédé de construction d'algorithmes de calcul approché des racines d'une équation du type f(x)=0, C.R. Acad. Sci. Paris 308 (1989) 433--436.
F. Cajori, Historical note on the Newton--Raphson method of approximation, Amer. Math. Monthly 18 (1911) 29--33.
F. Cajori, A History of Mathematics (Macmillan, New York, 2nd ed., 1919).
F. Cajori, An Introduction to the Modern Theory of Equations (Macmillan, New York, 1904).
B. Carnahan, H.A. Luther and J.O. Wilkes, Applied Numerical Methods (Wiley, New York, 1969) 141--209.
R. Carniel, A quasi cell mapping approach to the global dynamical analysis of Newton's root-finding algorithm, Appl. Numer. Math. 15 (1994) 133--152.
J. Carnoy, Cours d'Algèbre supérieure (Gauthier-Villars, Paris, 1900).
V. Casulli and D. Trigiante, Multipoint iterative parallel methods for solving equations, Calcolo 15 (1978) 147--160.
V. Casulli and D. Trigiante, Sui procedimenti iterativi composti, Calcolo 13 (1976) 403--420.
A. Cauchy, Sur la résolution numérique des équations, in: Oeuvres Complètes Sér. 2 3 (Gauthier-Villars, Paris, 1897) 378--425.
A. Cauchy, Sur la résolution numérique des équations algébriques et transcendantes, C.R. Acad. Sci. Paris 11 (1840) 829--847.
A. Cauchy, Sur la résolution des équations numériques et sur la théorie d'élimination, in: Oeuvres Complètes Sér. 2 9 (Gauthier-Villars, Paris, 1891) 87--161.
A. Cauchy, Sur la determination approximative des racines d'une équation algébrique ou transcendante, in: Oeuvres Complètes Sér. 2 4 (Gauthier-Villars, Paris, 1899) 573--609.
A. Cayley, Sur les racines d'une équation algébriques, C.R. Acad. Sci. Paris 110 (1890) 215--218.
A. Cayley, Application of the Newton--Fourier method to an imaginary root of an equation, Quart. J. Pure Appl. Math. 16 (1879) 179--185.
A. Cayley, The Newton--Fourier imaginary problem, Amer. J. Math. 2 (1879) 97.
M.N. Chanabasappa, A note on the computation of multiple zeros of polynomials by Newton's method, BIT 19 (1979) 134--135.
H.A. Chase, A note on the rate of convergence of Newton's method, Appl. Anal. 14 (1982) 55--60.
H.A. Chase, Alternate convergence criteria for iterative methods of nonlinear equations, J. Franklin Inst. 317 (1984) 89--103.
D. Chen, Kantorovich--Ostrowski convergence theorems and optimal error bounds for Jarratt's iterative method, Internat. J. Comput. Math. 31 (1990) 221--235.
D. Chen, On the convergence and optimal error estimates of King's iteration procedures for solving nonlinear equations, Internat. J. Comput. Math. 26 (1989) 229--237.
D.M. Claudio, An algorithm for solving nonlinear equations based on the regula falsi and Newton methods, Z. Angew. Math. Mech. 64 (1984) T407--T408.
D.M. Claudio, Hybrid interval algorithms and their Implementation on the HP-25, Z. Angew. Math. Mech. 66 (1986) T294--T296.
D.B. Clegg, On Newton's method with a class of rational functions, J. Comput. Appl. Math. 7 (2) (1981) 93--100.
K.J. Cohen, Certification of Algorithm 30, Comm. ACM 5 (1962) 50.
L. Collatz, Monotonie und Extremalprinzipien beim Newtonschen Verfahren, Numer. Math. 3 (1961) 99--106.
L. Collatz, Das vereinfachte Newtonsche Verfahren bei algebraischen und transzendenten Gleichungen, Z. Angew. Math. Mech. 34 (1954) 70--71.
L. Collatz, Numerische und graphische Methoden, Handbuch der Physik 2, Berlin (1955) 370--382.
L. Collatz et al., Eds., Functional Analysis and Numerical Mathematics (Academic Press, New York, 1966).
L. Collatz, Funktionanalysis und Numerische Mathematik (Springer, Berlin, 1964).
M. Cosnard and C. Masse, Convergence presque partout de la méthode de Newton, C.R. Acad. Sci. Paris Sér. A 297 (1983) 549--552.
J.H. Curry, L. Garnett and D. Sullivan, On the iteration of a rational function: computer experiments with Newton's method, Comm. Math. Phys. 91 (1983) 267--277.
A. Cuyt, in: A. Cuyt and L. Wuytack, Eds., Nonlinear Methods in Numerical Analysis, North-Holland Math. Stud. 136, Stud. Comput. Math. 1 (North-Holland, Amsterdam, 1987) 220--237.
B. Döring, Über das Newtonsche Näherungs-Verfahren, Math.-Phys. Semesterber. 16 (1963) 27--40.
H. Dörrie, Praktische Algebra (Oldenbourg, München, 1959).
M. Darboux, Sur la méthode d'approximation de Newton, Nouv. Ann. Math. Ser. 2 8 (1869) 11--27.
R.H. Dargel, F.H. Loscalzo and T.H. Witt, Automatic error bounds on real zeros of rational functions, Comm. ACM 9 (1966) 806--809.
M. Davies and B. Dawson, Globally convergent monotonic suppression techniques for automatic root finders in vibration analysis, Internat. J. Numer. Methods Engrg. 23 (1986) 25--34.
J.E. Dawson, A formula approximatting the root of a function, Inst. Math. Appl. J. Numer. Anal. 2 (1982) 371--375.
T.J. Dekker, Newton--Laguerre iteration, in: Colloq. Internat. CNRS No. 165, Programmation en Mathématiques Numériques (1968) 189--200.
J.E. Dennis and R.B. Schnabel, Numerical Methods for Unconstrained Optimization and Non-linear Equations (Prentice-Hall, Englewood Cliffs, NJ, 1983).
J.I. Derr, A unified process for the evaluation of the zeros of polynomials over the complex field, Math. Tables Aids Comput. 13 (1959) 29--36.
L. Derwidué, Introduction à l'algèbre supérieure et au calcul numérique algébrique, Masson et Cie, Paris (1957).
G. Di Lena and D. Trigante, Metodo di Euler e ricerva delle radici di una equazione, Calcolo 13 (1976) 377--396; Calcolo 14 (1977) 121--131.
L.E. Dickson, Elementary Theory of Equations (Wiley, New York, 1914).
L.E. Dickson, First Course in the Theory of Equations (Wiley, New York, 1922).
L.E. Dickson, New First Course in the Theory of Equations (Wiley, New York, 1952).
J. Dieudonné, Calcul Infinitésimal (Hermann, Paris, 1968).
N.S. Dimitrova and S.M. Markov, Interval methods of Newton type for nonlinear equations, PLISKA Stud. Math. Bulgar. 5 (1983) 105--117.
D. Dobbs and R. Hanks, A modern course on the theory of equations (Polygonal Publishers., 2nd ed., 1992).
D.E. Dobbs and R. Hanks, A Modern Course on the Theory of Equations (Polygonal Publ. House, Passic, NJ, 1980).
C. Domb, On iterative solutions of algebraic equations, Proc. Cambridge Philos. Soc. 45 (1949) 237--240.
C. Dong, A Family of multipoint iterative methods for finding multiple roots of equations, Internat. J. Comput. Math. 21 (1987) 363--367.
G.C. Donovan, A.R. Miller and T.J. Moreland, Pathological functions for Newton's method, Amer. Math. Monthly 100 53--58.
A. Douady and J. Hubbard, On the dynamics of polynomial-like mappings, Ann. Sci. École Norm. Sup. 18 (1985) 287--343.
D.K. Dunaway, A composite algorithm for finding zeros of real polynomials, Ph.D. Thesis, Southern Methodist Univ., Dallas, TX, 1972.
I.E. Durand, Solutions Numérique des Équations Algébriques. Tome I: Équations du Type F(x)=0; Racines d'une Polynôme (Masson, Paris, 1960) 279--281.
C.V. Durell and A. Robson, Advanced Algebra, Vols. 1, 2 (Bell, London, 1936--1937).
J. Dvorchuk, Factorization of a polynomial into quadratic factors by Newton's method, Apl. Mat. 14 (1969) 54--80.
J.P. Eckmann, Savez-vous résoudre z3-1?, La Recherche 14 (1983) 260--262.
K.W. Ellenberger, Algorithm 30: Numerical solution of the polynomial equation, Comm. ACM 3 (1960) 643.
K.W. Ellenberger, On programming the numerical solution of polynomial equations, Comm. ACM 3 (1960) 644--647.
R.A. Fairthorne, Solution of quadratics with real roots, Math. Gaz. 26 (1942) 109--110.
G. Fatou, Sur les équations fonctionnelles I, Bull. Soc. Math. France 47 (1919) 161--271; II, ibid. 48 (1920) 33--94; III, 208--314.
H.B. Fine, On Newton's method of approximation, U.S. Proc. Nat. Acad. Sci. 2 (1916) 546--552.
M. Flexor and P. Sentenac, Algorithmes de Newton généralisés, C.R. Acad. Sci. Paris 308 (1989) 445--448.
L.R. Ford, The solution of equations by the method of successive approximations, Amer. Math. Monthly 32 (1925) 272--287.
G.E. Forsythe, M.A. Malcolm and C.B. Moler, Computer Methods for Mathematical Computation (Prentice Hall, Englewood Cliffs, NJ, 1977) 156--168.
G.E. Forsythe, Singularity and near singularity in numerical analysis, Amer. Math. Monthly 65 (1958) 229--240.
J.B.J. Fourier, Oeuvres, 2 (Gauthier-Villars, Paris, 1890) 243--253.
J.B.J. Fourier, Analyse des Équations Détermines (Didot, Paris, 1831).
C.E. Fröberg, Introduction to Numerical Analysis (Addison-Wesley, Reading, MA, 1969).
J. Friedman, On the convergence of Newton's method, J. Complexity 5 (1989) 12--33.
J. Friedman, On Newton's method for polynomials, in: 27th Annual Symp. on Foundations of Computer Science (1986) 153--161.
J. Friedman, A density theorem for purely iterative zero finding methods, SIAM J. Comput. 19 (1990) 124--132.
J. Friedman, Random polynomials and approximate zeros of Newton's method, SIAM J. Comput. 19 (1990) 1068--1099.
G.S. Ganshin, Extension of the convergence region of Newton's method, U.S.S.R. Comput. Math. and Math. Phys. 11 (5) 249--252.
I. Gargantini, Comparing parallel Newton's method with parallel Laguerre's method, Comput. Math. Appl. 2 (1976) 201--206.
C.F. Gerald, Applied Numerical Analysis (Addison-Wesley, Reading, MA, 1984) 1--79.
J. Gerlach, Accelerated convergence in Newton's method, SIAM Rev. 36 (1994) 272--276.
J.B. Gibson, Optimal rational starting approximations, J. Approx. Theory 12 (1974) 182--189.
G. Glatz, Newton-Algorithmen zur Bestimmung von Polynomwurzeln unter Verwendung komplexer Kreisarithmetik, in: K. Nickel, Ed., Interval Mathematics (Springer, Berlin 1975) 205--214.
H.H. Goldstine, A History of Numerical Analysis from the 16th Through the 19th Centuries (Springer, New York, 1977).
J.V. Gonçalves, Sur le méthode de Newton, Univ. Lisbon Fac. Ci. A. Ci. Mat. (2) 3 (1954) 191--196.
R.L. Goodstein and T.A. Broadbent, The convergence of iterative processes, J. London Math. Soc. 22 (1947) 168--171.
S. Gorn, Maximal convergence intervals and a Gibbs type phenomenon for Newton's approximation procedure, Ann. of Math. (2) 59 (1954) 463--476.
J.A. Grant and G.D. Hitchins, The solution of polynomial equations in interval arithmetic, Comput. J. 16 (1973) 69--72.
D. Greenspan, On popular methods and extant problems in the solution of polynomial equations, Math. Mag. 31 (1957--1958) 239--253.
L.W. Griffiths, Introduction to the Theory of Equations (Wiley, New York, 1945).
D. Grohne, Bemerkungen zur Erweiterung des Verfahrens von Newton--Raphson auf die Berechnung einer mehrfachen Nullstelle, Z. Angew. Math. Mech. 37 (1957) 233.
O.H. Hald, On a Newton--Moser type method, Numer. Math. 23 (1975) 411--426.
H.J. Hamilton, Roots of equations by functional iteration, Duke Math. J. 13 (1946) 113--121.
R.W. Hamming, Introduction to Applied Numerical Analysis (McGraw-Hill, New York, 1971).
E. Hansen, Interval forms of Newton's method, Computing 20 (1978) 153--165.
E. Hansen, A globally convergent interval method for computing and bounding real roots, BIT 18 (1978) 415--424.
E. Hansen and M. Patrick, Estimating the multiplicity of a root, Numer. Math. 27 (1976) 121--131.
E.R. Hansen, On solving systems of equations using interval arithmetic, Math. Comp. 22 (1968) 374--384.
R.J. Hanson, Automatic error bounds for real roots of polynomials having interval coefficients, Comput. J. 13 (1970) 284--288.
P. Hartman, Newtonian approximations to a zero of a function, Comment. Math. Helv. 21 (1949) 321--326.
D.R. Hartree, Notes on iterative processes, Proc. Cambridge Philos. Soc. 45 (1949) 230--236.
J. Heinz, Polynom-Nullstellen mit dem Rechenstab, Praxis Math. 5 (4) (1963) 97--99.
W. Heitzinger, I. Troch and G. Valentin, Praxis Nichtlinearer Gleichungen (Hanser Verlag, München, 1985).
P. Henrici, Essentials of Numerical Analysis (Wiley, New York, 1982) 90--103; 136--168.
P. Henrici, Circular arithmetic and the determination of polynomial zeros, in: J.L. Morris, Ed., Conference on Applications of Numerical Analysis, Lecture Notes in Math. 228 (Springer, Berlin, 1971) 86--92.
P. Henrici, Applied and Computational Complex Analysis (Wiley, New York, 1977).
P. Henrici, Quotient-difference algorithms, in: A. Ralston and H.S. Wilf, Eds., Mathematical Methods for Digital Computers, Vol. II (Wiley, New York, 1967) 35--62.
P. Henrici, Elements of Numerical Analysis (Wiley, New York, 1964) 79--81; 99--101; 305--309.
J. Herzberger, Über Matrixdarstellungen für Iterationsverfahren bei nichtlinearen Gleichungen, Computing 12 (1974) 215--222.
J. Herzberger, Multipoint-Iterationsformeln hoher Ordnung zur Einschliessung von reellen Nullstellen, Z. Angew. Math. Mech. 62 (1982) T331.
J. Herzberger, Über ein intervallmässiges Newton-Verfahren, Z. Angew. Math. Mech. 66 (1986) T413--T415.
J. Herzberger, On the R-order of some recurrences with applications to inclusion-methods, Computing 36 (1986) 175--180.
J. Herzberger, Bemerkungen zu einem Verfahren von R.E. Moore, Z. Angew. Math. Mech. 53 (1973) 356--358.
J. Hines, On approximating the roots of an equation by iteration, Math. Mag. 24 (1951) 123--127.
M.W. Hirsch and S. Smale, On algorithms for solving f(x)=0, Comm. Pure Appl. Math. 32 (1979) 281--312.
U. Hochstrasser, Numerical methods for finding solutions of nonlinear equations, in: J. Todd, Ed., Survey of Numerical Analysis (McGraw-Hill, New York, 1962) 255--278.
D.J. Hopgood, Improved root-finding methods derived from inverse interpolation, J. Inst. Math. Appl. 14 (1974) 217--228.
R.W. Hornbeck, Numerical Methods (Quantum, New York, 1975).
W.G. Horner, Approximation to the roots of algebraic equations in a series of aliquot parts, Quart. J. Pure Appl. Math. 3 (1860) 251--262.
W.G. Horner, A new method of solving numerical equations of all orders by continuous approximation, Philos. Trans. Roy. Soc. London 109 (1819) 308--335.
W.G. Horner, On algebraic transformation, The Mathematician 1 (1845) 108--112; 136--142; 311--316.
A.S. Householder, The Numerical Treatment of a Single Nonlinear Equation (McGraw-Hill, New York, 1970).
A.S. Householder, Principles of Numerical Analysis (McGraw-Hill, New York, 1953) 86--132.
M. Hurley, Attracting orbits in Newton's method, Trans. Amer. Math. Soc. 297 (1986) 143--158.
M. Hurley and C. Martin, Newton's algorithm and chaotic dynamical systems, SIAM J. Math. Anal. 15 (1984) 238--252.
M. Igarashi, A termination criterion for iterative methods used to find the zeros of polynomials, Math. Comp. 42 (1984) 165--171.
M. Igarashi, Zeros of polynomials and an estimation of its accuracy, J. Inform. Process. 5 (1982) 172--175.
M. Igarashi, Practical problems arising for finding roots of nonlinear equations, Appl. Numer. Math. 1 (1985) 433--455.
E. Isaacson and H.B. Keller, Analysis of Numerical Methods (Wiley, New York, 1966) 85--133.
P. Jarratt, Multipoint iterative methods for solving certain equations, Comput. J. 8 (1966) 398--400.
P. Jarratt, Some fourth order multipoint iterative methods for solving equations, Math. Comp. 20 (1966) 434--437.
P. Jarratt, A review of methods for solving nonlinear algebraic equations in one variable, in: P. Rabinowitz, Ed., Numerical Methods for Nonlinear Algebraic Equations (Gordon and Breach, New York, 1970) 1--26.
H. Jeffries, Numerical solution of equations, Math. Gaz. 27 (1943) 20.
H. Jeffries, Numerical solution of algebraic equations, Nature 119 (1927) 565.
W. Jennings, First Course in Numerical Methods (MacMillan, New York, 1964) 5--12; 23--39.
L.W. Johnson and R.D. Riess, Numerical Analysis (Addison-Wesley, Reading, MA, 1982) 142--201.
R.L. Johnston, Numerical Methods: A Software Approach (Wiley, New York, 1982).
G. Joseph, A. Levine and J. Liukkonen, Randomized Newton--Raphson, Appl. Math. Comput. 6 (1990) 459--469.
G. Julia, Mémoire sur l'itération des fonctions rationelles, J. Math. Pures Appl. 4 (1918) 47--245.
J. Kiefer, Optimum sequential search and approximation methods under minimum regularity assumptions, J. Soc. Indust. Appl. Math. 5 (1957) 105--136.
M. Kim, On approximate zeros and root-finding algorithms for a complex polynomial, Math. Comp. 51 (1988) 707--719.
M.H. Kim, On approximate zeros and root-finding algorithms for a complex polynomial, Math. Comp. 51 (1988) 707--719.
C. Kimberling, Microcomputer-assisted mathematics: Roots: Newton's method, Math. Teacher 78 (1985) 626--629.
R.F. King, A fifth-order family of modified Newton methods, BIT 11 (1971) 409--412.
R.F. King, An extrapolation method of order four for linear sequences, SIAM J. Numer. Anal. 16 (1979) 719--725.
R.F. King, Anderson--Björk for linear sequences, Math. Comp. 41 (1983) 591--596.
R.F. King, Improving the Van de Vel root-finding method, Computing 30 (1983) 373--378.
R.F. King, An efficient one-point extrapolation method for linear convergence, Math. Comp. 35 (1980) 1285--1290.
R.F. King, Tangent methods for nonlinear equations, Numer. Math. 18 (1972) 298--304.
R.F. King, A family of fourth order methods for nonlinear equations, SIAM J. Numer. Anal. 10 (1973) 876--879.
I. Kiss, Über eine Verallgemeinerung des Newtonschen Näherungsverfahrens, Z. Angew. Math. Mech. 34 (1954) 68--69.
W. Kizner, A numerical method for finding solutions of nonlinear equations, J. Soc. Indust. Appl. Math. 12 (1964) 424--428.
T.I. Kogan, Construction of iteration processes of high orders, Zh. Vychisl. Mat. i Mat. Fiz. 7 (1967) 423--424.
W. Kotzé, Notes on numerical analysis, IV. On accelerating iteration procedures with superlinear convergence, Canad. Math. Bull. 7 (1964) 425--430.
R. Krawczyk and A. Neumaier, Interval slopes for rational functions and associated centered form, SIAM J. Numer. Anal. 22 (1985) 604--616.
R. Krawczyk, Newton-Algorithmen zur Bestimmung von Nullstellen mit Fehlerschranken, Computing 4 (1969) 187--201.
R. Krawczyk, Einschliebung von Nullstellen mit Hilfe einer Intervallarithmetik, Computing 5 (1970) 356--370.
R. Krawczyk, Abbrechkriterium für Iterationsverfahren, Z. Angew. Math. Mech. 52 (1972) 227--232.
L.I. Kronsjö, Algorithms: Their Complexity and Efficiency (Wiley, Chichester, 1979) 10--89.
H.W. Kuhn, Z. Wang and S. Xu, On the cost of computing roots of polynomials, Math. Programming 28 (1984) 156--164.
U. Kulisch and W.L. Miranker, Eds., A New Approach to Scientific Computation (Academic Press, New York, 1983) 42--45; 99--104; 121--137.
H.T. Kung, Synchronized and asynchronous parallel algorithms for multiprocessors, in: J.F. Traub, Ed., Algorithms and Complexity: New Directions and Recent Results (Academic Press, New York, 1976) 153--200.
H.T. Kung and J.F. Traub, Optimal order and efficiency for iterations with two evaluations, SIAM J. Numer. Anal. 13 (1976) 84--99.
H.T. Kung and J.F. Traub, Optimal order of one-point and multi-point iteration, J. Assoc. Comput. Mach. 21 (1974) 643--651.
H.T. Kung and J.F. Traub, Computational complexity of one-point and multi-point iteration, in: R.M. Karp, Ed., Complexity of Computation (Amer. Mathematical Soc., Providence, RI, 1974) 149--160.
H.T. Kung and J.F. Traub, All algebraic functions can be computed fast, J. Assoc. Comput. Mach. 25 (1978) 245--260.
H.T. Kung, The complexity of obtaining starting points for solving operator equations by Newton's method, in: J.F. Traub, Ed., Analytic Computational Complexity (Academic Press, New York, 1976) 35--57.
K.S. Kunz, Numerical Analysis (McGraw-Hill, New York, 1957) 1--37.
S.S. Kuo, Computer Applications of Numerical Methods (Addison-Wesley, Reading, MA, 1972).
V.A. Kurchatov, The method of linearized residuals for accelerating the convergence of an iteration method, Sov. Math. (Iz. VUZ) 23 (8) (1979) 34--45.
A.G. Kurosh, Algebraic Equations of Arbitrary Degree, Little Math. Lib. (Mir, Moscow, 1977).
H.L. Lagouanelle, Sur une méthode de calcul de l'ordre de multiplicité des zéros d'un polynôme, C.R. Acad. Sci. Paris A 262 (1966) 626--627.
J.L. Lagrange, De la résolution des équations numériques de tous les degrés, in: Oeuvres, Vol. 8 (Gauthier-Villars, Paris, 1879).
E. Laguerre, Sur la résolution des équations numériques, Nouv. Ann. Math. Ser. 2 17 (1878) 20--25; 97--104; also: Oeuvres, Vol. 1 (Gauthier-Villars, Paris, 1898) 52--63.
E.N. Laguerre, Sur une formule nouvelle permettant d'obtenir,... les racines d'une équation..., in: Oeuvres, Vol. 1 (Gauthier-Villars, Paris, 1898) 51.
P. Lancaster, Error analysis for the Newton--Raphson method, Numer. Math. 9 (1966) 55--68.
P. Lancaster, Convergence of the Newton--Raphson method for arbitrary polynomials, Math. Gaz. 48 (1964) 291--295.
G.N. Lance, Numerical Methods for High Speed Computers (Iliffe, London, 1960) 123--137.
C. Lanczos, Applied Analysis (Prentice-Hall, Englewood Cliffs, NJ, 1956) 5--48.
J.M. Lane and R.F. Riesenfeld, Bounds on a polynomial, BIT 21 (1981) 112--117.
F.M. Larkin, A modification of the secant rule derived from a maximum likelihood principle, BIT 19 (1979) 214--222.
M. Lauer, Generalized p-adic constructions, SIAM J. Comput. 12 (1983) 395--410.
C.C. Lee and H.P. Niu, Determination of zeros of polynomials by synthetic division, Internat. J. Comput. Math. 7 (1979) 131--140.
J.A.N. Lee, Numerical Analysis for Computers (Reinhold, New York, 1966) Chapter 9.
E. Lehaye, Une méthode de résolution d'une catégorie d'équations transcendantes, C.R. Acad. Sci. Paris 198 1840--1842.
G.R. Lindfield and J.E.T. Penny, Microcomputers in Numerical Analysis (Wiley, New York, 1989) Chapter 2.
S. Linnaimaa, Combatting the effects of under- and over-flow in determining real roots of polynomials, SIGNUM 16 (2) (1981) 11--15.
J. Lipson, Newton's method: A great algebraic algorithm, in: R.D. Jenks, Ed., Proc. 1976 ACM Symp. on Symbolic and Algebraic Computation (1976) 260--270.
I.M. Longman, On the utility of Newton's method for computing complex roots of equations, Math. Tables Aids Comput. 14 (1960) 187--189.
W.V. Lovitt, Elementary Theory of Equations (Prentice-Hall, New York, 1939).
R. Ludwig, Über Iterationsverfahren für Gleichungen und Gleichungssysteme, Z. Angew. Math. Mech. 34 (1954) 210--225; 404--416.
H.A. Luther, A class of iterative techniques for the factorization of polynomials, Comm. ACM 7 (1964) 177--179.
C.C. MacDuffee, Theory of Equations (Wiley, New York, 1954) Chapter 7.
D. Mackie and T. Scott, Pitfalls in the use of computers for the Newton--Raphson method, Math. Gaz. 69 (1985) 252--257.
N. Macon, Numerical Analysis (Wiley, New York, 1963).
H.J. Maehly, Zur iterativen Auflösung algebraischer Gleichungen, Z. Angew. Math. Phys. 5 (1954) 260--263.
G.D. Majstrovskii, On the optimality of Newton's method, Soviet Math. Dokl. 13 (1972) 838--840.
W.R. Mann, Averaging to improve convergence of iterative processes, in: M.Z. Nashed, Ed., Functional Methods in Numerical Analysis (Springer, New York, 1979) 169--179.
A. Manning, How to be sure of solving a complex polynomial using Newton's method, Bol. Soc. Brasil Mat. 22 (1992) 157--177.
I. Manning, A method for improving iteration procedures, Proc. Cambridge Philos. Soc. 63 (1967) 183--186.
A. Marin, Géométrie des polynômes. Coût global de la méthode de Newton, Sém. Bourbaki 670 (1986).
D.D. McCracken and W.S. Dorn, Numerical Methods and Fortran Programming (Wiley, New York, 1965).
C. McMullen, Families of rational maps and iterative root-finding algorithms, Ann. Math. 125 (1987) 467--494.
G. Meinardus and G.D. Taylor, Optimal partitioning of Newton's method for calculating roots, Math. Comp. 35 (1980) 1221--1230.
W.E. Milne, Numerical Calculus (Princeton, 1949).
R.E. Moore, Introduction to algebraic problems, in: E. Hansen, Ed., Topics in Interval Analysis (Oxford Univ. Press, Oxford, 1969) 3--10.
R.E. Moore, Interval Analysis (Prentice-Hall, Englewood Cliffs, NJ, 1960) Section 7.2.
R.M. Moore, Methods and Applications of Interval Analysis, SIAM Studies in Applied Mathematics, Philadelphia (1979).
E.J. Mordell, Newton's work in pure mathematics, Nature 119 (1927) Supp. 42.
S. Moritsugu, A. Furukawa, H. Kobayashi and T. Sasaki, On the power series solutions of a system of algebraic equations, SIGSAM Bull. 21 (4) (1987) 14--23.
T.E. Mott, Newton's method and multiple roots, Amer. Math. Monthly 64 (1957) 635--638.
D.G. Moursund, Optimal starting values for the Newton--Raphson calculation of &sqrt;x, Comm. ACM 10 (1967) 430--432.
I. Munro, Some results concerning efficient and optimal algorithms, in: Third Annual ACM Symp. on the Theory of Computers, Shaker Heights (1971) 40--44.
T. Murakami, Some fifth-order multipoint iterative formulae for solving equations, J. Inform. Process. 1 (1978) 138--139.
P. Myrberg, Sur l'itération des polynômes réels quadratiques, J. Math. Pures Appl. 41 (1962) 339--351.
P.F. Nesdore, The determination of an algorithm which uses the mixed strategy technique for the solution of a single nonlinear equation, in: P. Rabinowitz, Ed., Numerical Methods for Nonlinear Algebraic Equations (Gordon and Breach, London, 1970) 27--45.
B. Neta, A sixth order family of methods for nonlinear equations, Internat. J. Comput. Math. 7 (1979) 157--161.
B. Neta, On a family of multipoint methods for nonlinear equations, Internat. J. Comput. Math. 9 (1981) 353--361.
B. Neta, A new iterative method for the solution of systems of nonlinear equations, in: Z. Ziegler, Ed., Proc. Conf. on Approximation Theory and Applications (1981) 249--263.
E. Netto, Vorlesungen über Algebra (Teubner, Leipzig, 1896).
I. Newton, De Analysi per Aequationes Numero Terminorum Infinitas (1669).
I. Newton, in: Horsley, Ed., Collected Works, Vol. I (1779) 268--271.
K. Nickel, Triplex-Algol and its applications, in: E. Hansen, Ed., Topics in Interval Analysis (Clarendon Press, Oxford, 1969) 10--24.
K. Nickel, A globally convergent ball Newton method, SIAM J. Numer. Anal. 18 (1981) 988--1003.
K.L. Nielsen, Methods in Numerical analysis (McMillan, New York, 1964).
Anon, Nine chapters of the mathematical art, in: J. Needham, Ed., Science and Civilization in China (Cambridge Univ. Press, Cambridge, 1954) 126--127.
I. Ninomiya, Best rational starting approximations and improved Newton iteration for the square root, Math. Comp. 24 (1970) 391--404.
F.W.J. Olver, The evaluation of zeros of high-degree polynomials, Philos. Trans. Roy. Soc. London Ser. A 244 (1952) 385--415.
A. Ostrowski, Über einen Fall der Konvergenz des Newtonschen Näherungsverfahrens, Rec. Math. 3 (1938) 254--258.
A. Ostrowski, Über die Konvergenz und die Abrundungsfestigkeit des Newtonschen Verfahrens, Rec. Math. 2 (1937) 1073--1095.
A. Ostrowski, A method of speeding up iterations with super-linear convergence, J. Math. Mech. 7 (1958) 117--120.
A.M. Ostrowski, Solution of Equations and Systems of Equations (Academic Press, New York, 2nd ed., 1966).
A.M. Ostrowski, A method for automatic solution of algebraic equations, in: B. Dejon and P. Henrici, Eds., Constructive Aspects of the Fundamental Equation of Algebra (Wiley/Interscience, New York, 1969) 209--224.
J.-P. Francoise, Estimations uniforms pour le domaines de convergence de la méthode de Newton, in: J.J. Risler, Ed., Séminaire de Géométrie Algébrique Réelle, 24 (Publ. Univ. Paris VII, Paris, 1986).
V.Y. Pan, Sequential and parallel complexity of approximate evaluation of polynomial zeros, Comput. Math. Appl. 14 (1987) 591--622.
M.L. Patrick, A highly parallel algorithm for approximating all zeros of a polynomial with only real zeros, Comm. ACM 15 (1972) 952--955.
M.L. Patrick and D. Saari, A globally convergent algorithm for determining approximate real zeros of a class of functions, BIT 15 (1975) 296--303.
R.N. Pederson, Newton's method and the Jenkins--Traub algorithm, Proc. Amer. Math. Soc. 97 (1986) 687--690.
H.O. Peitgen, D. Saupe and S.V.Haeseler, Cayley's problem and Julia sets, Math. Intelligencer 6 (2) (1984) 11--20.
J. Peltier, Résolutions Numérique des Équations Algébriques (Paris, 1957).
M.S. Petkovic and J. Herzberger, Hybrid inclusion algorithms for polynomial multiple complex zeros in rectangular arithmetic, Appl. Numer. Math. 7 (1991) 241--262.
M.S. Petkovic, On an interval Newton's method derived from exponential curve fitting, Z. Angew. Math. Mech. 61 (1981) 117--119.
M.S. Petkovic, Some interval iterations for finding a zero of a polynomial with error bounds, Comput. Math. Appl. 14 (1987) 479--495.
A. Peyerimhoff, E. Stickel and E. Wirsing, On the rate of convergence for two-term recursions, Computing 40 (1988) 329--335.
E. Pflanz, Über ein Verallgemeinerung des Verfahrens der Kombination von Newtonscher Methode und Regula falsi zur Auflösung einer Gleichung f(x)=0, Z. Angew. Math. Mech. 28 (1948) 114--122.
NATIONAL PHYSICAL LABORATORY, Modern Computing Methods, Her Majesty's Stationary Office, London (1961).
S.M. Pizer, Numerical Computing and Mathematical Analysis (Science Research Assoc., New York, 1975) 175--250.
T. Pomentale, Homotopy iterative methods for polynomial equations, J. Inst. Math. Appl. 13 (1974) 201--213.
D.B. Popovski, A note on King's fifth order family of methods for solving equations, BIT 21 (1981) 129--130.
F.A. Potra, Efficient hybrid algorithms for finding zeros of convex functions, J. Complexity 10 (1994) 199--215.
F.A. Potra and V. Pták, Nondiscrete Induction and Iterative Processes (Pitman, London, 1984).
M.D. Presic, On Ostrowski's fundamental existence theorem in the complex case, Publ. Inst. Math. (Beograd) (N.S.) 26 (40) (1979) 229--232.
M.D. Presic, On Ostrowski's fundamental existence theorem, Publ. Inst. Math. (Beograd) 24 (38) (1978) 125--133.
W.H. Press, B.P. Flannery, S.A. Teukolsky and W.T. Vetterling, Numerical Recipes-the Art of Scientific Computing (Cambridge University Press, New York, 1986) 240--273.
A.V. Prokopchenko, Iterative processes of high order, U.S.S.R. Comput. Math. and Math. Phys. 14 (1) (1974) 229--231.
V. Pták, Rate of convergence of Newton's process, Numer. Math. 25 (1976) 279--285.
V. Pták, Concerning the rate of convergence of Newton's process, Comment. Math. Univ. Carolin. 16 (1975) 699--705.
A. Rényi, On Newton's method of approximation, Mat. Lapok 1 (1950) 278--293.
L.B. Rall, Computational Solution of Nonlinear Operator Equations (Wiley, New York, 1969).
L.R. Rall, Convergence of the Newton process to multiple solutions, Numer. Math. 9 (1966) 23--37.
A. Ralston and P. Rabinowitz, A First Course in Numerical Analysis (McGraw-Hill, New York, 2nd ed., 1987) 354.
?. Raphson, Analysis Aequationum Universalis (London, 1690).
J. Renegar, On the cost of approximating all roots of a complex polynomial, Math. Programming 32 (1985) 319--336.
J.R. Rice, Numerical Methods, Software and Analysis (McGraw-Hill, New York, 1983) 217--264.
J.R. Rice and S. Rosen, NAPSS -- a numerical analysis problem solving system, in: Proc. ACM 21st National Conf. (1966) 51--56.
J.R. Rice, Matrix representations of nonlinear equation iterations---application to parallel computation, Math. Comp. 25 (1971) 639--647.
H.W. Richmond, On certain formulae for numerical approximation, J. London Math. Soc. 19 (1944) 31--38.
J. Rokne, Optimal computation of the Bernstein algorithm for the bound of an interval polynomial, Computing 28 (1982) 239--246.
J. Rokne, Automatic errorbounds for simple zeros of analytic functions, Comm. ACM 16 (1973) 101--104.
J. Rokne and P. Lancaster, Automatic errorbounds for the approximate solution of equations, Computing 4 (1969) 294.
J. Rokne, Errorbounds for simple zeros of λ-matrices, Computing 16 (1976) 17--27.
P. Romanowsky, Theorie der sukzessiven Newtonschen Annäherungen, Z. Angew. Math. Mech. 9 (1929) 420--421.
T.S. Roy et al., A new method to solve non-linear equations, Inform. Process. Lett. 50 (1994) 75--79.
P. Rufini, Sopra la Determinazione delle Radici (Modena, 1804).
C. Runge, Separation und Approximation der Wurzeln, in: Encyklopädie der Mathematischen Wissenschaften, I, 1 (Teubner, Leipzig, 1898) 404--448.
C. Runge, Praxis der Gleichungen (De Gruyter, Berlin, 1921).
C. Runge and H. König, Vorlesungen über Numerisches Rechnen (Springer, Berlin, 1924) 150--176.
H. Rutishauser, Eine Konvergenzverbesserung für die Newtonsche Methode, Z. Angew. Math. Phys. 1 (1950) 211--212.
D.G. Saari and J.B. Urenko, Newton's method, circle maps, and chaotic motion, Amer. Math. Monthly 91 (1984) 3--17.
D.G. Saari, Some informational requirements for convergence, J. Complexity 3 (1987) 302--311.
M.G. Salvadori and M.L. Baron, Numerical Methods in Engineering (Prentice Hall, New York, 1952).
P.A. Samuelson, Iterative computation of complex roots, J. Math. and Phys. 28 (1949) 259--267.
H. Sanden, Practical Mathematical Analysis, translation: H. Levy (Methuen, London, 1923).
J.B. Scarborough, Numerical Mathematical Analysis (Johns Hopkins Univ. Press, Baltimore, MD, 1968) Chapters 8, 10, 11.
A. Schönhage, Equation solving in terms of computational complexity, in: Proc. Internat. Congress Math., Berkeley, CA (1986) 131--153.
U. Schendel, Introduction to Numerical Methods for Parallel Computers (Wiley, New York, 1984) 105--118.
C.E. Schmidt and L.R. Rabiner, A study of techniques for finding the zeros of linear phase FIR digital filters, IEEE Trans. Acoust. Speech Signal Process. 25 (1977) 96--98.
E. Schröder, Über unendlich viele Algorithmen zur Auflösung der Gleichungen, Math. Ann. 2 (1870) 317--365.
J. Schröder, Factorization of polynomials by generalized Newton procedures, in: B. Dejon and P. Henrici, Eds., Constructive Aspects of the Fundamental Theorem of Algebra (Wiley/Interscience, New York, 1969) 295--320.
L.F. Shampine and R.C. Allen, Numerical Computing: An Introduction (Saunders, Philadelphia, PA, 1973) 87--108; 242--245.
H.S. Sharp, A comparison of methods for evaluating the complex roots of quartic equations, J. Math. and Phys. 20 (3) (1941) 249--250.
G.S. Shedler, Parallel numerical methods for the solution of equations, Comm. ACM 10 (5) (1967) 286--291.
M. Shub, D. Tischler and R.F. Williams, The Newtonian graph of a complex polynomial, SIAM J. Math. Anal. 19 (1988) 246--256.
M. Shub and S. Smale, Computational complexity: on the geometry of polynomials and a theory of cost II, SIAM J. Comput. 15 (1986) 145--161.
M. Shub and S. Smale, Computational complexity; on the geometry of polynomials and a theory of cost I, Ann. Sci. École Norm. Sup. (4) 18 (1985).
W. Sibagaki, On the idea of "numerical convergence" and its some applications, Mem. Fac. Sci. Kyushu Univ. Ser. A 5 (1950) 89--97.
D.M. Simeunovic, Sur une evaluation des valeurs approximatives des zéros complexes des polynômes, Mat. Vesnik 13 (28) (1976) 449--454.
J. Singer, Elements of Numerical Analysis (Academic Press, London, 1964) 137--199.
S. Smale, Newton estimates from data at one point, in: Proc. Conf. in Honour of Gail Young (Springer, New York, 1986) 185--196.
S. Smale, On the efficiency of the algorithms of analysis, Bull. Amer. Math. Soc. (2) 13 (1985) 87--121.
S. Smale, The fundamental theorem of algebra and complexity theory, Bull. Amer. Math. Soc. (2) 4 (1981) 1--36.
V.I. Smirnov, A Course of Higher Mathematics, Vol. I (Pergamon, Oxford, 1964) 480--505.
W.F. Smyth, The construction of rational iteration functions, Math. Comp. 32 (1978) 811--827.
R.W. Snyder, One more correction formula, Amer. Math. Monthly 62 (1955) 722--725.
P.A. Stark, Introduction to Numerical Methods (Macmillan, New York, 1970) 68--122.
R.S. Stepleman, A characterization of local convergence for fixed point iterations in R1, SIAM J. Numer. Anal. 12 (1975) 887--894.
P.H. Sterbenz and C.T. Fike, Optimal starting approximations for Newton's method, Math. Comp. 23 (1969) 313--318.
G.W. Stewart, On a companion operator for analytic functions, Numer. Math. 18 (1971) 26--43.
E.L. Stiefel, An Introduction to Numerical Mathematics (Academic Press, New York, 1963).
J. Stoer and R. Bulirsch, Introduction to Numerical Analysis (Springer, New York, 1980) 270--299.
W.M. Stone, A form of Newton's method with cubic convergence, Quart. Appl. Math. 11 (1953) 118--119.
D.J. Struik, Ed., A Source Book in Mathematics, 1200--1800 (Harvard Univ. Press, Cambridge, MA, 1969).
F. Stummel and K. Hainer, Introduction to Numerical Analysis, translation: E.R. Dawson (Scottish Academic Press, 1980) 19--35.
C.T. Sullivan, A rational transformation of the complex plane with applications to the roots of polynomials, Trans. Roy. Soc. Canada (3) 30 (1936) 31--39.
D. Sullivan, Conformal dynamical systems, in: Geometric Dynamics, Lecture Notes in Math. 1007 (Springer, Berlin, 1983) 1725--1752.
Z. Szabó, Über Gleichungslösende Iterationen ohne Divergenzpunkt I, III, Publ. Math. Debrecen 20 (1973) 223--233; 27 (1980) 185--200.
Z. Szabó, Newton-parabola combined method for solving equations, in: C. Brezinski and U. Kulisch, Eds., Computational and Applied Mathematics I (North-Holland, Amsterdam, 1992) 447--452.
Z. Szabó, Combined iteration method for solving equations, in: D. Greenspan, Ed., Numerical Methods, Miscolc, Colloquia Mathematica Societatis Janos Bolyai 50 (North-Holland, Amsterdam, 1986) 581---588.
A. Tauber, Über die Newton'sche Näherungsmethode, Monatsh. Math. 6 (1895) 291--302.
G.D. Taylor, Optimal starting approximations for Newton's method, J. Approx. Theory 3 (1970) 156--163.
M. Tienari, On the control of floating-point mantissa length in iterative computations, in: A. Gunther, B. Levrat and H. Lipps, Eds., International Computing Symposium (Elsevier, New York, 1974) 315--322.
O.N. Tikhonov, A generalization of Newton's method of computing the roots of algebraic polynomials, Soviet Math. (Iz. VUZ) 20 (6) (1976) 109--111.
J. Todd, Basic Numerical Mathematics, Vol. 1: Numerical Mathematics (Birkhäuser, Basel, 1979).
I. Todhunter, Theory of Equations (Macmillan, London, 1882).
J.F. Traub, The solution of transcendental equations, in: A. Ralston and H.S. Wilf, Eds., Mathematical Methods for Digital Computers, Vol. II (Wiley, New York, 1967) 171--184.
J.F. Traub, Iterative Methods for the Solution of Equations (Prentice-Hall, Englewood Cliffs, NJ, 1964); (Chelsea, New York, 1982).
J.F. Traub, Theory of optimal algorithms, in: D.J. Evans, Ed., Software for Numerical Mathematics (Academic Press, New York, 1974) 1--13.
J.F. Traub, On Newton--Raphson iteration, Amer. Math. Monthly 74 (1967) 996--998.
J.F. Traub, Computational complexity of iterative processes, SIAM J. Comput. 1 (1972) 167--179.
H.W. Turnbull, Theory of Equations (Oliver and Boyd, Edinburgh, 1939) 72.
M. Urabe, Error estimation in numerical solution of equations by iteration process, J. Sci. Hiroshima Univ. Ser. A-I 26 (1962) 77--91.
J. Urenko, Improbability of nonconvergent chaos in Newton's method, J. Math. Anal. Appl. 117 (1986) 42--47.
J.V. Uspensky, Theory of Equations (McGraw-Hill, New York, 1948).
H. Van de Vel, A method for computing a root of a single nonlinear equation including its multiplicity, Computing 14 (1975) 167--171.
J.S. Vandergraft, Introduction to Numerical Computations (Prentice-Hall, Englewood Cliffs, NJ, 1964).
P. Verbaeten, Computing real zeros of polynomials with SAC-2, SIGSAM Bull. (ACM) 9 (2) (1975) 8--10; 24.
H.D. Victory and B. Neta, A higher order method for multiple zeros of nonlinear functions, Internat. J. Comput. Math. 12 (1983) 329--335.
F. Vieta, De Numerosa Protestatum Purarum atque Adfectarum ad Exegesim Resolutione Tractatus (1600).
J. Vignes, New methods for evaluating the validity of the results of mathematical computations, Math. Comput. Simulation 20 (4) (1978) 227--249.
A. Vogel, Iterationsverfahren zur Auflösung einer Gleichung f(x)=0, Praxis Math. 1 (1959) 197--200.
R. Voigt, Orders of convergence for iterative procedures, SIAM J. Numer. Anal. 8 (1971) 222--243.
J. Von zur Gathen, Hensel and Newton methods in valuation rings, Math. Comp. 42 (1984) 637--661.
E.R. Vrscay and W.J. Gilbert, Extraneous fixed points, basin boundaries and chaotic dynamics for Schröder and König rational iteration functions, Numer. Math. 52 (1988) 1--16.
E.R. Vrscay, Julia sets and Mandelbrot-like sets associated with higher order Schröder rational iteration functions: a computer assisted study, Math. Comp. (1986) 151--169.
A.-W.M. Nourein, Root determination by use of Padé approximants, BIT 16 (1976) 291--297.
R. Wait, The Numerical Solution of Algebraic Equations (Wiley, Chichester, 1979).
D.D. Wall, The order of an iteration formula, Math. Tables Aids Comput. 10 (1956) 167--168.
?. Wallis, Algebra (1685) Chapter 94.
Z. Wang and S. Xu, Approximate zeros and computational complexity theory, Sci. Sinica Ser. A 27 (1984) 566--575.
E. Waring, Meditationes Algebraicae (Cambridge Univ. Press, Cambridge, 1770) 54--77.
H. Weber, Traité d'Algèbra Supérieure (Gauthier-Villars, Paris, 1898).
H. Weber, Lehrbuch der Algebra (Chelsea, New York).
W. Werner, Some efficient algorithms for the solution of a single nonlinear equation, Internat. J. Comput. Math. 9 (1981) 141--149.
W. Werner, Some supplementary results on the 1+&sqrt;2 order method for the solution of nonlinear equations, Numer. Math. 38 (1982) 383--392.
W. Werner, Über ein Verfahren der Ordnung 1+&sqrt;2 zur Nullstellenbestimmung, Numer. Math. 32 (1979) 333--342.
W. Werner, Some improvement of classical iterative methods for the solution of nonlinear equations, in: E.L. Allgower, K. Glashoff and N.-O. Peitgen, Eds., Proc. Numerical Solution of Nonlinear Equations (Springer, Bremen, 1980) 426--440.
W. Werner, Iterationsverfahren höherer Ordnung zur Lösung nichtlinearer Gleichungen, Z. Angew. Math. Mech. 61 (1981) T322--T324.
E.T. Whittaker and G. Robinson, The Calculus of Observations (London, 4th ed., 1944) 78--131.
H.S. Wilf, Mathematics for the Physical Sciences (Wiley, New York, 1962) 82--107.
H.S. Wilf, The numerical solution of polynomial equations, in: A. Ralston and H.S. Wilf, Eds., Mathematical Methods for Digital Computers (Wiley, New York, 1960) 233--241.
J.H. Wilkinson, The evaluation of the zeros of ill-conditioned polynomials. Parts I and II, Numer. Math. 1 (1959) 150--180.
J.H. Wilkinson, Rounding Errors in Algebraic Processes (Prentice-Hall, Englewood Cliffs, NJ, 1963) 34--78.
F.A. Willers, Zum Newtonschen Näherungsverfahren, Z. Angew. Math. Mech. 16 (1936) 315--316.
F.A. Willers, Practical Analysis (Dover, New York, 1948) 205--265.
M.A. Wolfe, Interval methods for algebraic equations, in: R.E. Moore, Ed., Reliability in Computing. International Workshop on the Role of Interval Mathematics in Scientific Computing (Academic Press, New York, 1988).
S. Wong, Newton's method and symbolic dynamics, Proc. Amer. Math. Soc. 91 (1984) 245--253.
W. Xing-Hua and Z. Shi-ming, The quasi-Newton method in parallel circular iteration, J. Comput. Math. 3 305--309.
W. Xing-hua, On the convergence of King--Werner's iteration procedures for solving nonlinear equations, Math. Numer. Sinica 4 (1982) 70--79.
W. Xing-hua, On the error estimates for some numerical root-finding methods, Acta Math. Sinica 22 (1979) 638--642.
T. Yamamoto, Error bounds for Newton's process derived from the Kantorovich theorem, Japan J. Appl. Math. 2 (1985) .
Y. Ye, Combining binary search and Newton's method to compute real roots for a class of real functions, J. Complexity 10 (1994) 271--280.
J. Yohe, Interval bounds for square roots and cube roots, Computing 11 (1973) 51--53.
D.M. Young and R.T. Gregory, A Survey of Numerical Mathematics, Vol. I (Addison-Wesley, Reading, MA, 1972) 93--245.
T.J. Ypma, Finding a multiple zero by transformations and Newton-like methods, SIAM Rev. 25 (1983) 365--378.
D.Y.Y. Yun, Algebraic algorithms using p-adic constructions, in: R.D. Jenks, Ed., Proc. 1976 ACM Symp. on Symbolic and Algebraic Computation (1976) 248--259.
V.L. Zaguskin, Handbook of Numerical Methods for the Solution of Algebraic and Transcendental Equations (Pergamon, Oxford, 1961).
A. Zajta, Untersuchungen über die Verallgemeinerung der Newton--Raphsonschen Wurzelapproximation, Acta Tech. Acad. Sci. Hungar. 15 (1956) 233--260; ibid. 19 (1957) 25--60.
R. Zippel, Newton's iteration and the sparse Hensel algorithm, in: P.S. Wang, Ed., Proc. 1981 ACM Symp. on Symbolic and Algebraic Computation (Assoc. Computing Machinery, New York, 1981) 68--72.
S. Zuhe and M.A. Wolfe, A ball Newton point algorithm for bounding zeros of analytic functions, Appl. Math. Comput. 36 (1990) 1--14.
R. Zurmühl, Praktische Mathematik (Springer, Berlin, 1971).