G. Alefeld, F.A. Potra and Y. Spi, On enclosing simple roots of nonlinear equations, Math. Comp. 61 (1993) 733--744.
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.E. Alefeld and F.A. Potra, Some efficient methods for enclosing simple zeros of nonlinear equations, BIT 32 (1992) 334--344.
B.W. Arden and K.N. Astill, Numerical Algorithms: Origins and Applications (Addison-Wesley, Reading, MA, 1970) 54--80.
K. Atkinson, An Introduction to Numerical Analysis (Wiley, New York, 1978) 39--106.
E.J. Barbeau, Polynomials (Springer, New York, 1989).
E. Barnes and W.L. Miranker, An application of optimal control theory to equation solving, in: Proc. IEEE Conf. on Decision and Control (1976) 543--547.
A. Benjamin, The bisection method: which root?, Amer. Math. Monthly 94 (1987) 861--863.
I.S. Berezin and N.P. Zhidkov, Computing Methods, Vol. 2 (Pergamon Press, Oxford, 1965) Chapter 7.
A. Björck and G. Dahlquist, Numerical Methods (Prentice-Hall, Englewood Cliffs, NJ, 1974).
R.S. Booth, Random search for zeros, J. Math. Anal. Appl. 20 (1967) 239--257.
R. Brent, Algorithms for Minimization without Derivatives (Prentice-Hall, Englewood Cliffs, NJ, 1973) 49, 58.
R. Brent, An algorithm with guaranteed convergence for finding a zero of a function, Comput. J. 14 (1971) 422--425.
J.C.P. Bus and T.J. Dekker, Two efficient algorithms with guaranteed convergence for finding a zero of a function, ACM Trans. Math. Software 1 (1975) 330--345.
A. Cauchy, Méthode général pour la détermination des racines réelles des équations algébriques ou même transcendantes, in: Oeuvres Complètes Sér. 1 4 (Gauthier-Villars, Paris, 1884) 88--98.
A. Cauchy, Sur la résolution numérique des équations, in: Oeuvres Complètes Sér. 2 3 (Gauthier-Villars, Paris, 1897) 378--425.
F.L. Chernousko, An optimal algorithm for finding the roots of an approximately computed function, U.S.S.R. Comput. Math. and Math. Phys. 8 (4) (1968) 1--23.
H.H.Y. Chien, A multiphase algorithm for single variable equation solving, J. Inst. Math. Appl. 9 (1972) 290--298.
N. Chuquet, Le triparty en la science des nombres (Lyons, 1484), Bull. Boncompagni 8 (1880) 653--654.
G.E. Collins and R.G.K. Loos, Real zeros of polynomials, Comput. Suppl. 4 (1982) 83--94.
G. Corliss, Which root does the bisection algorithm find?, SIAM Rev. 19 (1977) 325--327.
M.G. Cox, A bracketing technique for computing a zero of a function, Comput. J. 13 (1970) 101--102.
J.E. Dawson, A formula approximatting the root of a function, Inst. Math. Appl. J. Numer. Anal. 2 (1982) 371--375.
J.C. Dekker, Zeroin, in: B. Dejon and P. Henrici, Eds., Constructive Aspects of the Fundamental Theorem of Algebra (Wiley/Interscience, New York, 1969).
T.J. Dekker, Finding a zero by means of successive linear interpolation, in: B. Dejon and P. Henrici, Eds., Constructive Aspects of the Fundamental Theorem of Algebra (Wiley/Interscience, New York, 1969) 37--48.
T.J. Dekker, Correctness proof and machine arithmetic, in: B. Fosdick and L. Dudley, Eds., Performance Evaluation of Numerical Software (Elsevier, Amsterdam, 1979) 31--44.
J.E. Dennis and R.B. Schnabel, Numerical Methods for Unconstrained Optimization and Non-linear Equations (Prentice-Hall, Englewood Cliffs, NJ, 1983).
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).
M. Dowell and P. Jarratt, The "Pegasus" method for computing the root of an equation, BIT 12 (1972) 503--508.
M. Dowell and P. Jarratt, A modified reguli falsi method for computing the root of an equation, BIT 11 (1971) 168--174.
O. Eriksen and J. Staunstrup, Concurrent algorithms for root searching, Acta. Inform. 18 (1983) 361--376.
A. Finbow, The bisection method: a best case analysis, Amer. Math. Monthly 92 (1985) 285--286.
G.E. Forsythe, Remarks on the paper by Dekker, in: B. Dejon and P. Henrici, Eds., Constructive Aspects of the Fundamental Theorem of Algebra (Wiley/Interscience, New York, 1969).
G.E. Forsythe, M.A. Malcolm and C.B. Moler, Computer Methods for Mathematical Computation (Prentice Hall, Englewood Cliffs, NJ, 1977) 156--168.
S.W. Gal and W.L. Miranker, Optimal sequential and parallel search for finding a root, J. Combin. Theory Ser. A 23 (1977) 1--4.
L.E. Garey and R.E. Shaw, A Steffensen-type method for computing a root, Internat. J. Comput. Math. 18 (1985) 185--190.
C.F. Gerald, Applied Numerical Analysis (Addison-Wesley, Reading, MA, 1984) 1--79.
G.H. Gonnet, On the structure of zero finders, BIT 17 (1977) 170--183.
G.H. Gonnet, A short note on convergence near a high-order zero, BIT 16 (1976) 338--339.
S. Graf, E. Novak and A. Papageorgiou, Bisection is not optimal on the average, Numer. Math. 55 (1989) 481--491.
J.A. Grant and G.D. Hitchins, The solution of polynomial equations in interval arithmetic, Comput. J. 16 (1973) 69--72.
O. Gross and S.M. Johnson, Sequential minimax search for the zero of a convex function, Math. Tables Aids Comput. 13 (1959).
H.S. Hall and S.R. Knight, Higher Algebra (Macmillan, London, 1960) 83--96; 452--489.
R.W. Hamming, Introduction to Applied Numerical Analysis (McGraw-Hill, New York, 1971).
R.W. Hamming, Numerical Methods for Scientists and Engineers (McGraw-Hill, New York, 1962) 356--359.
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.
J. Herzberger, Some multipoint-iteration methods for bracketting a zero with application to parallel computation, in: M. Feilmeier, Ed., Parallel Computers---Parallel Mathematics (North-Holland, Amsterdam, 1977) 231--234.
R.W. Hornbeck, Numerical Methods (Quantum, New York, 1975).
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).
B. Jones, A heuristic for root isolation, Internat. J. Numer. Methods Engrg. 11 (1977) 598--603.
B. Jones, M. Banerjee and L. Jones, Root isolation for transcendental equations, Comput. J. 27 (1984) 184--187.
B. Jones, W.G. Waller and A. Feldman, Root isolation using function values, BIT 18 (1978) 311--319.
L.P. Jones, Root isolation methods based upon Lagrangian interpolation, Internat. J. Comput. Math. 24 (1988) 343--355.
W. Kahan, Personal calculator adds key to solve any equation f(x)=0, Hewlett-Packard J. (December 1979) 20--26.
I.N. Katz and M.A. Franklin, Two strategies for root finding on multiprocessor systems, SIAM J. Sci. Statist. Comput. 6 (1985) 314--333.
E.H. Kaufman and T.D. Lenker, Linear convergence and the bisection algorithm, Amer. Math. Monthly 93 (1986) 48--51.
J. Kiefer, Optimum sequential search and approximation methods under minimum regularity assumptions, J. Soc. Indust. Appl. Math. 5 (1957) 105--136.
C. Kimberling, Microcomputer-assisted mathematics: Roots: half-interval search, Math. Teacher 78 (1985) 120--123.
A.S. Kozek and A. Trzmielak-Stanislawska, On dependence of MR- and MM-algorithms upon the value of switching control variable CTR, J. Comput. Appl. Math. 23 (1) (1988) 109--115.
A.S. Kozek and A. Trzmielak-Stanislawska, On a class of omnibus algorithms for zero-finding, J. Complexity 5 (1989) 80--95.
R. Krautstengel, On one iterative method of calculating a single root of equation f(x)=0, U.S.S.R. Comput. Math. and Math. Phys. 8 (6) (1968) 186--188.
G.K. Kristiansen, Zeros of arbitrary function, BIT 3 (1963) 205--206.
G.K. Kristiansen, A rootfinder using a monotone rational approximation, SIAM J. Sci. Statist. Comput. 6 (1985) 118--127.
L.I. Kronsjö, Algorithms: Their Complexity and Efficiency (Wiley, Chichester, 1979) 10--89.
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.
S.S. Kuo, Computer Applications of Numerical Methods (Addison-Wesley, Reading, MA, 1972).
J.M. Lane and R.F. Riesenfeld, Bounds on a polynomial, BIT 21 (1981) 112--117.
D. Le, An efficient derivative-free method for solving nonlinear equations, ACM Trans. Math. Software 11 (1985) 250--262; correction: ibid. 15 (1989) 287.
D. Le, Three new rapidly convergent algorithms for finding a zero of a function, SIAM J. Sci. Statist. Comput. 6 (1985) 193--208.
G.R. Lindfield and J.E.T. Penny, Microcomputers in Numerical Analysis (Wiley, New York, 1989) Chapter 2.
W.V. Lovitt, Elementary Theory of Equations (Prentice-Hall, New York, 1939).
C.A. Michelli and W.L. Miranker, High order search methods for finding roots, J. Assoc. Comput. Mach. 22 (1975) 51--60.
D. Nerinckx and A. Hagemans, A comparison of non-linear equation solvers, J. Comput. Appl. Math. 2 (2) (1976) 145--148.
K. Nickel, Die vollautomatische Berechnung einer einfachen Nullstelle von F(t)=0 einschlieblich einer Fehlerabschätzung, Computing 2 (1967) 232--245.
V. Norton, Algorithm 631: Finding a bracketed zero by Larkin's method of rational interpolation, ACM Trans. Math. Software 11 (1985) 120--134.
V. Norton, Remark on algorithm 631, ACM Trans. Math. Software 12 (1986) 72.
E. Novak, Average-case results for zero finding, J. Complexity 5 (1989) 489--501.
K. Ozawa, Some globally convergent iterative methods based on the bisection iteration for solving scalar equations, Comput. Math. Appl. 28 (6) (1994) 83--91.
G. Peters and J.H. Wilkinson, Eigenvalues of Ax = λBx with band-symmetric A and B, Comput. J. 12 (1969) 398--404.
S.M. Pizer, Numerical Computing and Mathematical Analysis (Science Research Assoc., New York, 1975) 175--250.
D.B. Popovski, A note on King's method F for finding a bracketed root, Computing 29 (1982) 355--359.
F.A. Potra, Efficient hybrid algorithms for finding zeros of convex functions, J. Complexity 10 (1994) 199--215.
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.
J.R. Rice, Numerical Methods, Software and Analysis (McGraw-Hill, New York, 1983) 217--264.
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.
L.F. Shampine and R.C. Allen, Numerical Computing: An Introduction (Saunders, Philadelphia, PA, 1973) 87--108; 242--245.
G.S. Shedler and M.M. Lehman, Evaluation of redundancy in a parallel algorithm, IBM Systems J. 6 (1967) 142--149.
R.I. Shrager, A rapid robust rootfinder, Math. Comp. 44 (1985) 151--165.
K. Sikorski, Bisection is optimal, Numer. Math. 40 (1982) 11--117.
K. Sikorski and G.M. Trojan, Asymptotic near optimality of the bisection method, Numer. Math. 57 (1990) 421--433.
P.A. Stark, Introduction to Numerical Methods (Macmillan, New York, 1970) 68--122.
J. Stoer and R. Bulirsch, Introduction to Numerical Analysis (Springer, New York, 1980) 270--299.
F. Stummel and K. Hainer, Introduction to Numerical Analysis, translation: E.R. Dawson (Scottish Academic Press, 1980) 19--35.
A.G. Sukharev, Optimal search for the roots of a function satisfying a Lipschitz condition, U.S.S.R. Comput. Math. and Math. Phys. 16 (1) (1976) 17--26.
A. Swift and G.R. Lindfield, Comparison of a continuation method with Brent's method for the numerical solution of a single non-linear equation, Comput. J. 21 (1978) 359--362.
J. Traub and H. Wozniakowski, A General Theory of Optimal Algorithms (Academic Press, New York, 1980) 150--172.
J.F. Traub and H. Wozniakowski, Information and Computation, in: Adv. Comput. 23 (Academic Press, New York, 1984) 35--92.
J.F. Traub, G.W. Wasilkowski and H. Wozniakowski, Information, Uncertainty, Complexity (Addison-Wesley, Reading, MA, 1983).
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.
R. Wait, The Numerical Solution of Algebraic Equations (Wiley, Chichester, 1979).
H. Wozniakowski, A survey of information-based complexity, J. Complexity 1 (1985) 11--44.
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.
D.M. Young and R.T. Gregory, A Survey of Numerical Mathematics, Vol. I (Addison-Wesley, Reading, MA, 1972) 93--245.