Laguerre-like inclusion method for polynomial zeros

Journal of Computational and Applied Mathematics

Volumn 152, Issue 1-2, 2003, Pages 451-465

  Petković, Miodrag S ^a  

^a UNIVERSITY OF NI   (Serbia)

Author keywords

Circular arithmetic; Convergence rate; Inclusion of polynomial zeros; Laguerre like methods; Simultaneous methods

Indexed keywords

COMPUTATIONAL METHODS; CONVERGENCE OF NUMERICAL METHODS; ITERATIVE METHODS;

POLYNOMIAL ZEROS;

POLYNOMIALS;

MATHEMATICAL ANALYSIS;

EID: 0037334660     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(02)00723-9     Document Type: Article

References (17)

1. G. Alefeld, J. Herzberger, Introduction to Interval Computations, Academic Press, New York, 1983.
2. C. Carstensen, M.S. Petković, An improvement of Gargantini's simultaneous inclusion method for polynomial roots by Schroeder's correction, Appl.Numer.Math.13 (1994) 453-468.
3. I. Gargantini, Parallel Laguerre iterations: complex case, Numer. Math. 26 (1976) 317-323.
4. I. Gargantini, Further application of circular arithmetic: Schröder-like algorithms with error bound for finding zeros of polynomials, SIAM J. Numer. Anal. 15 (1978) 497-510.
5. I. Gargantini, P. Henrici, Circular arithmetic and the determination of polynomial zeros, Numer. Math. 18 (1972) 305-320.
6. E. Hansen, M. Patrick, A family of root finding methods, Numer. Math. 27 (1977) 257-269.
7. E. Hansen, M. Patrick, J. Rusnak, Some modifications of Laguerre's method, BIT 17 (1977) 409-417.
8. P. Henrici, Applied and Computational Complex Analysis, Vol. I, Wiley, New York, 1974.
9. A.M. Ostrowski, Solution of Equations in Euclidean and Banach Space, Academic Press, New York, 1973.
10. B. Parlett, Laguerre's method applied to the matrix eigenvalue problem, Math. Comp. 18 (1964) 464-485.
11. M.S. Petković, On a generalization of the root iterations for polynomial complex zeros in circular interval arithmetic, Computing 27 (1981) 37-55.
12. M.S. Petković, Iterative Methods for Simultaneous Inclusion of Polynomial Zeros, Springer, Berlin, Heidelberg, New York, 1989.
13. M.S. Petković, Halley-like method with corrections for the inclusion of polynomial zeros, Computing 62 (1999) 69-88.
14. M.S. Petković, C. Carstensen, On some improved inclusion methods for polynomial roots with Weierstrass' corrections, Comput. Math. Appls. 25 (1993) 59-67.
15. M.S. Petković, Lj.D. Petković, Complex Interval Arithmetic and its Applications, Wiley-VCH, Berlin, Weinheim, New York, 1998.
16. M.S. Petković, Lj. Petković, D. Źivković, Laguerre-like methods for the simultaneous approximation of polynomial zeros, Computing 15 (Suppl) (2001) 189-209.
17. J. Stoer, R. Bulirsch, Einführung in die Numerische Mathematik II, Springer, Berlin, 1973.