A computational comparison of the first nine members of a determinantal family of root-finding methods

Journal of Computational and Applied Mathematics

Volumn 130, Issue 1-2, 2001, Pages 197-204

  Kalantari, Bahman ^a   Park, Seungyoung ^a  

^a RUTGERS UNIVERSITY   (United States)

Author keywords

Order of convergence; Polynomial zeros

Indexed keywords

COMPUTATIONAL COMPLEXITY; POLYNOMIALS;

NEWTON METHOD; ROOT-FINDING ITERATION FUNCTIONS;

ITERATIVE METHODS;

MATHEMATICAL METHOD;

EID: 0035336353     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(99)00383-0     Document Type: Article

References (12)

1. B. Kalantari, Generalization of Taylor's theorem and Newton's method via a new family of determinantal interpolation formulas and its applications, J. Comput. Appl. Math. 126 (2000) 287-318.
2. B. Kalantari, Approximation of polynomial root using a single input and the corresponding derivative values, Technical Report DCS-TR 369, Department of Computer Science, Rutgers University, New Brunswick, NJ, 1998.
3. B. Kalantari, Halley's method as the first member of an infinite family of cubic order root-finding methods, Technical Report DCS-TR 370, Department of Computer Science, Rutgers University, New Brunswick, NJ, 1998.
4. B. Kalantari, On the order of a determinantal family of root-finding methods, BIT 39 (1999) 96-109.
5. B. Kalantari, J. Gerlach, Newton's method and generation of a determinantal family of iteration functions, J. Comput. Appl. Math. 116 (2000) 195-200.
6. B. Kalantari, I. Kalantari, High order iterative methods for approximating square roots, BIT 36 (1996) 395-399.
7. B. Kalantari, I. Kalantari, R. Zaare-Nahandi, A basic family of iteration functions for polynomial root finding and its characterizations, J. Comput. Appl. Math. 80 (1997) 209-226.
8. J.M. McNamee, A bibliography on root of polynomials, J. Comput. Appl. Math. 47 (1993) 391-394.
9. V.Y. Pan, Solving a polynomial equation: some history and recent progress, SIAM Rev. 39 (1997) 187-220.
10. T.R. Scavo, J.B. Thoo, On the geometry of Halley's method, Amer. Math. Monthly 102 (1995) 417-426.
11. J.F. Traub, Iterative Methods for the Solution of Equations, Prentice-Hall, Englewood Cliffs, NJ, 1964.
12. T.J. Ypma, Historical development of Newton-Raphson method, SIAM Rev. 37 (1995) 531-551.