L. Atanassova, On the R-order of a single-step Nourein type method, in: L. Atanassova and J. Herzberger, Eds., Computer Arithmetic and Enclosure Methods (Elsevier, 1992) 179--187.
D. Bini, Complexity of parallel polynomial computations, in: D.J. Evans, Ed., Parallel Computation: Methods, Algorithms and Applications (Adam Hilger, 1989) 115--126.
D. Bini and L. Gemignani, On the complexity of polynomial zeros, SIAM J. Comput. 21 (1992) 781--799.
E. Bodewig, Konvergenztypen und das Verhalten von Approximationen in der Nähe einer mehrfachen Wurzel einer Gleichung, Z. Angew. Math. Mech. 29 (1949) 44--51.
A. Borodin and I. Munro, The Computational Complexity of Algebraic and Numerical Problems (Elsevier, New York, 1977) 54--76; 132--137; 148--150.
R. Brent, S. Winograd and P. Wolfe, Optimal iterative processes for root-finding, Numer. Math. 20 (1973) 327--341.
W. Burmeister and J.W. Schmidt, On the R-Order of Coupled Sequences, Parts II and III, Computing 29 (1982) 73--81; 30 (1984) 157--169.
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.
V. Casulli and D. Trigiante, Sui procedimenti iterativi composti, Calcolo 13 (1976) 403--420.
V. Casulli and D. Trigiante, Computational complexity for a class of multipoint iterative procedures without or with internal memory, Calcolo 14 (1977) 225--235.
H.A. Chase, A note on the rate of convergence of Newton's method, Appl. Anal. 14 (1982) 55--60.
P. Chen, Approximate zeros of quadratically convergent algorithms, Math. Comp. 63 (1994) 247--270.
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.
G.E. Collins, Computer algebra of polynomials and rational functions, Amer. Math. Monthly 80 (1973) 725--755.
K. Datta, On the parallel arithmetic complexity of the root-finding problem, Internat. J. Comput. Math. 22 (1987) 99--104.
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).
G.C. Donovan, A.R. Miller and T.J. Moreland, Pathological functions for Newton's method, Amer. Math. Monthly 100 53--58.
A. Feldstein and R.M. Firestone, A study of Ostrowski efficiency for composite iteration algorithms, in: Proc. 1969 ACM Nat. Conf. (Assoc. Comput. Machinery, New York, 1969) 147--155.
H. Friedman and K. Ko, Computational complexity of real functions, Theoret. Comput. Sci. 20 (1982) 323--352.
G. Gati, The complexity of solving polynomial equations by prime root extraction, SIAM J. Algebraic Discrete Methods 4 (1983) 70--71.
W.M. Gentleman, On the relevance of various cost models of complexity, in: J.F. Traub, Ed., Complexity of Sequential and Parallel Numerical Algorithms (Academic Press, New York, 1973).
J.A. Grant and A. Ghiatis, Determination of the zeros of a linear combination of Chebyshev polynomials, IMA J. Numer. Anal. 3 (1983) 193--206.
J. Herzberger, Bounds for R-order of certain iterative numerical processes, BIT 26 (1986) 259--262.
A.C. Hindmarsh, Optimality in a class of rootfinding algorithms, SIAM J. Numer. Anal. 9 (1972) 205--214.
J.W. Hong, How fast the algebraic approximation can be?, Sci. Sinica 29A (1986) 813--823.
E. Isaacson and H.B. Keller, Analysis of Numerical Methods (Wiley, New York, 1966) 85--133.
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.
R.L. Johnston, Numerical Methods: A Software Approach (Wiley, New York, 1982).
B. Kacewicz, An integral-interpolation iterative method for the solution of scalar equations, Numer. Math. 26 (1976) 355--365.
E. Kaltofen, D.R. Musser and B.D. Saunders, A generalized class of polynomials that are hard to factor, SIAM J. Comput. 12 (3) (1983) 473--483.
M. Kim, Topological complexity of a root-finding algorithm, J. Complexity 5 (1989) 331--344.
M.H. Kim, On approximate zeros and root-finding algorithms for a complex polynomial, Math. Comp. 51 (1988) 707--719.
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.
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.
H.T. Kung and J.F. Traub, Fast algorithms for algebraic functions, in: J.F. Traub, Ed., Algorithms and Complexity (Academic Press, New York, 1976) 473 (abstract).
H.T. Kung, The computational complexity of algebraic numbers, SIAM J. Numer. Anal. 12 (1975) 89--96.
H.T. Kung, A bound on the multiplicative efficiency of iteration, J. Comput. System Sci. 7 (1973) 334--342.
H. Levine, A lower bound for the topological complexity of poly(d,n), J. Complexity 5 (1989) 34--44.
C. McMullen, Families of rational maps and iterative root-finding algorithms, Ann. Math. 125 (1987) 467--494.
R. Meersman, Optimal use of information in certain iterative processes, in: J.F. Traub, Ed., Analytic Computational Complexity (Academic Press, New York, 1976) 109--125.
G.V. Milovanovic and M.S. Petkovic, Computational efficiency of the simultaneous methods for finding polynomial zeros: Estimation of efficiency, in: D. Herceg, Ed., Numerical Methods and Approximation Theory, Novi Sad, 1985, University of Novi Sad (1985) 83--88.
De Morgan, A proof of the existence of a root of every algebraic equation, Cambridge Philos. Soc. Trans. 10 (1858) 261--270.
C.A. Neff, Specified precision polynomial root isolation is in NC, in: Proc. 31st IEEE Symp. on Foundation of Computer Science (1990) 152--162; also: J. Comput. System Sci. 48 (1994) 429--463.
E. Novak and K. Ritter, Some complexity results for zero finding for univariate polynomials, J. Complexity 9 (1993) 15--40.
A. Ostrowski, A method of speeding up iterations with super-linear convergence, J. Math. Mech. 7 (1958) 117--120.
V. Pan, Complexity of computations with matrices and polynomials, SIAM Rev. 34 (1992) 225--262.
V.Y. Pan, Sequential and parallel complexity of approximate evaluation of polynomial zeros, Comput. Math. Appl. 14 (1987) 591--622.
V.Y. Pan, Algebraic complexity of computing polynomial zeros, Comput. Math. Appl. 14 (1987) 285--304.
V.Y. Pan, Fast and efficient algorithms for sequential and parallel evaluation of polynomial zeros and of matrix polynomials, in: Proc. 26th Annual IEEE Symp. on Foundation of Computer Sci., Portland, OR (1985) 522--533.
V.Y. Pan, New resultant inequalities and complex polynomial factorization, SIAM J. Comput. 23 (1994) 934--950.
M.S. Paterson, Efficient iterations for algebraic numbers, in: R.E. Miller and J.W. Thatcher, Eds., Complexity of Computer Computations (Plenum, New York, 1972) 41--52.
M.S. Petkovic, G.V. Milovanovic and L.V. Stefanovic, On the convergence order of an accelerated simultaneous method for polynomial complex zeros, Z. Angew. Math. Mech. 66 (1986) T428--429.
M.S. Petkovic and G.V. Milovanovic, Computational efficiency of the simultaneous methods for finding polynomial zeros: comparison of various algorithms, in: D. Herceg, Ed., Numerical Methods and Approximation Theory, Novi Sad, 1985, University of Novi Sad (1985) 89--94.
M.S. Petkovic, L.D. Petkovic and L.V. Stefanovic, On the R-order of a class of simultaneous iterative processes, Z. Angew. Math. Mech. 69 (1989) T199--201.
M.S. Petkovic and L.D. Petkovic, On the bounds of the R-order of some iterative methods, Z. Angew. Math. Mech. 69 (1989) T197--198.
F.A. Potra and V. Pták, Nondiscrete Induction and Iterative Processes (Pitman, London, 1984).
F.A. Potra, On a modified secant method, in: Analyse Numérique et le Théorie de l'Approximation, 8 (1979) 203--214.
F.A. Potra, On Q-order and R-order of convergence, J. Optim. Theory Appl. 63 (1989) 415--431.
V. Pták, What should be a rate of convergence, RAIRO Anal. Numer. 11 (1977) 279--286.
J. Renegar, On the cost of approximating all roots of a complex polynomial, Math. Programming 32 (1985) 319--336.
J. Renegar, On the complexity of a piece-wise linear algorithm for approximating roots of complex polynomials, Math. Programming 32 (1985) 301--318.
J. Renegar, Computational complexity of solving real algebraic formulae, in: Proc. of the International Congress of Mathematicians, Kyoto, 1990 (Springer, Berlin, 1991), 1595--1606.
J.R. Rice, Numerical Methods, Software and Analysis (McGraw-Hill, New York, 1983) 217--264.
D.G. Saari, Some informational requirements for convergence, J. Complexity 3 (1987) 302--311.
A. Schönhage, Equation solving in terms of computational complexity, in: Proc. Internat. Congress Math., Berkeley, CA (1986) 131--153.
J.W. Schmidt, On the R-order of coupled equations, Computing 26 (1981) 333--342.
H. Shub and S. Smale, On the existence of generally convergent algorithms, J. Complexity 2 (1986) 2--11.
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).
M. Shub and S. Smale, On the existence of generally convergent algorithms, J. Complexity 2 (1986) 2--11.
K. Sikorski and G.M. Trojan, Asymptotic near optimality of the bisection method, Numer. Math. 57 (1990) 421--433.
K. Sikorski, Optimal solution of nonlinear equations satisfying a Lipschitz condition, Numer. Math. 43 (1984) 225--240.
K. Sikorski and H. Wozniakowski, For which error criteria can we solve nonlinear equations?, J. Complexity 2 (1986) 163--178.
K. Sikorski, Study of linear information for classes of polynomial equations, Aequationes Math. 37 (1989) 1--14.
K. Sikorski, Optimal solution of nonlinear equations, J. Complexity 1 (1985) 197--209.
K. Sikorsky, For which error criteria can we solve nonlinear equations?, J. Complexity 2 (1986) 163--178.
S. Smale, The fundamental theorem of algebra and complexity theory, Bull. Amer. Math. Soc. (2) 4 (1981) 1--36.
S. Smale, On the topology of algorithms I, J. Complexity 3 (1987) 81--89.
S. Smale, Algorithms for solving equations, Proc. Internat. Congress Math., Berkeley, CA (1987) 172--195.
G.W. Stewart, On the convergence of multi-point iterations, Numer. Math. 68 (1994) 143--147.
J.F. Traub, G.W. Wasilkowski and H. Wozniakowski, Information, Uncertainty, Complexity (Addison-Wesley, Reading, MA, 1983).
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, Computational complexity of iterative processes, SIAM J. Comput. 1 (1972) 167--179.
J.F. Traub, Optimal iterative processes: Theorems and conjectures, in: Proc. IFIP Congress, Booklet TA-1 (1971) 1273--1277.
J.F. Traub, G.W. Wasilkowski and H. Wozniakowski, Information-Based Complexity (Academic Press, New York, 1988) 188--193.
J.F. Traub and H. Wozniakowski, Strict lower and upper bounds on iterative computational complexity, in: J.F. Traub, Ed., Analytic Computational Complexity (Academic Press, New York, 1976) 15--34.
J.F. Traub et al., From Topology to Computation: Proceedings of the SMALEFEST, M.W. Hirsch et al., Eds. (Springer, Berlin, 1993) 317--320; 359--367; 387--394; 395--418; 419--431.
J.M. Trojan, Tight bounds on the complexity index of one-point iterations, Comput. Math. Appl. 6 (1980) 433--441.
J.M. Trojan, How to decrease the combinatory complexity, Demonstratio Math. 11 (1978) 807--811.
P. Turan, The power sum method and the approximative solution of algebraic equations, Math. Comp. 29 (1975) 311--318.
J.S. Vandergraft, Introduction to Numerical Computations (Prentice-Hall, Englewood Cliffs, NJ, 1964).
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.
D. Wang and F. Zhao, Complexity analysis of a process for simultaneously obtaining all zeros of a polynomial, Computing 43 (1989) 187--197.
Z. Wang and S. Xu, Approximate zeros and computational complexity theory, Sci. Sinica Ser. A 27 (1984) 566--575.
G.W. Wasilkowski, Any iteration using linear information for polynomial equations has infinite complexity, Theoret. Comput. Sci. 22 (1983) 195--208.
G.W. Wasilkowski, The strength of non-stationary iteration, Aequationes Math. 24 (1981) 243--260.
G.W. Wasilkowski, n-evaluation conjecture for multipoint iterations for the solution of scalar nonlinear equations, J. Assoc. Comput. Mach. 28 (1981) 71--80.
G.W. Wasilkowski, Can any stationary iteration using linear information be globally convergent?, J. Assoc. Comput. Mach. 27 (1980) 263--269.
L.O. Weisner, Introduction to the Theory of Equations (Macmillan, New York, 1938).
A.G. Werschulz, Multipoint methods with memory using Hermitian information, in: Proc. 1979 Conf. on Information Science and Systems (Johns Hopkins Univ. Press, Baltimore, MD, 1979).
A.G. Werschulz, Maximal order for multipoint methods with memory using Hermitian information, Internat. J. Comput. Math. 9 (1981) 223--241.
S. Winograd, Parallel iteration methods, in: R.E. Miller and J.W. Thatcher, Eds., Complexity of Computer Computations (Plenum, New York, 1973) 53--60.
S. Winograd and P. Wolfe, On the rate of convergence of local iterative schemes, in: Z. Kohavi and A. Paz, Eds., Theory of Machines and Computations (Academic Press, New York, 1971) 67--70.
H. Wozniakowski, A survey of information-based complexity, J. Complexity 1 (1985) 11--44.
H. Wozniakowski, Maximal stationary iterative methods for the solution of operator equations, SIAM J. Numer. Anal. 11 (1974) 939--949.
H. Wozniakowski, Information-based complexity, in: J.F. Traub et al., Eds., Annual Reviews of Computer Science, Vol. 1 (Annual Reviews, Palo Alto, CA, 1986) 346--350.
H. Wozniakowski, Maximal order of multipoint iterations using n evaluations, in: J.F. Traub, Ed., Analytic Computational Complexity (Academic Press, New York, 1976) 75--108.
H. Wozniakowski, Properties of maximal order methods for the solution of nonlinear equations, Z. Angew. Math. Mech. 55 (1975) 268--271.
H. Wozniakowski, Generalized information and maximal order of iteration for operator equations, SIAM J. Numer. Anal. 12 (1975) 121--135.
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.