On the convergence of Wang-Zheng's method

Journal of Computational and Applied Mathematics

Volumn 91, Issue 1, 1998, Pages 123-135

  Petković, Miodrag S ^a   Herceg, Dorde D ^b  

^a UNIVERSITY OF NI   (Serbia)

^b UNIVERSITY OF NOVI SAD   (Serbia)

Author keywords

Convergence; Initial conditions; Point estimation; Polynomial zeros; Simultaneous methods; Wang Zheng's method

Indexed keywords

APPROXIMATION THEORY; CONVERGENCE OF NUMERICAL METHODS; POLES AND ZEROS; POLYNOMIALS;

POINT ESTIMATION; WANG-ZHENG METHOD;

ITERATIVE METHODS;

EID: 0032048990     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(98)00034-X     Document Type: Article

References (29)

1. [1] C. Carstensen, On quadratic-like convergence of the means for two methods for simultaneous rootfinding of polynomials, BIT 33 (1993) 64-73.
2. [2] P. Chen, Approximate zeros of quadratically convergent algorithms, Math. Comput. 63 (1994) 247-270.
3. [3] J. H. Curry, On zero finding methods of higher order from data at one point, J. Complexity 5 (1989) 219-237.
4. [4] M. R. Farmer, G. Loizou, Locating multiple zeros interactively, Comput. Math. Appl. 11 (1985) 595-603.
5. [5] 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.
6. [6] P. Hertrici, Applied and Computational Complex Analysis, vol. I, Wiley, New York, 1974.
7. [7] Dj. Herceg, An algorithm for localization of polynomial zeros in: R. Tošić, Z. Budimac, (Eds.), Proc. VIII Internat. Conf. on Logic and Computer Science, Institute of Novi Sad, Novi Sad, 1997, pp. 67-75.
8. [8] M. Kim, Ph.D. Thesis, City University of New York, New York, 1985.
9. [9] M. Kim, On approximate zeros and rootfinding algorithms for a complex polynomial, Math. Comput. 51 (1988) 707-719.
10. [10] S. Lakić, M. S. Petkovic, On the matrix square root, Z. Angew. Math. Mech. to appear.
11. [11] M. S. Petković, Iterative Methods for Simultaneous Inclusion of Polynomial Zeros, Springer, Berlin, 1989.
12. [12] M. S. Petković, On the Halley-like algorithms for the simultaneous approximation of polynomial complex zeros, SIAM J. Numer. Anal. 26 (1989) 740-763.
13. [13] M. S. Petković, On initial conditions for the convergence of simultaneous root finding methods. Computing 57 (1996) 163-177.
14. [14] M. S. Petković, C. Carstensen, M. Trajković, Weierstrass' formula and zero-finding methods, Numer. Math. 69 (1995) 353-372.
15. [15] M. S. Petković, D Herceg, Point estimation and safe convergence of root-finding simultaneous methods, Scientific Rev. 21-22 (1996) 117-130.
16. [16] M. S. Petković, D Herceg, Börsch-Supan-like methods: Point estimation and parallel implementation. Intern. J. Comput. Math. 64 (1997) 327-341.
17. [17] M. S. Petković, D Herceg, S. Ilić, Point Estimation Theory and its Applications, Institute of Mathematics, Novi Sad, 1997.
18. [18] M. S. Petković, D. Herceg, S. Ilić, Point estimation and some applications to iterative methods, BIT, to appear.
19. [19] M. S. Petković, D. Herceg, S. Ilić, Safe convergence of simultaneous methods for polynomial zeros, submitted.
20. [20] M. S. Petković, S. Ilic, Point estimation and the convergence of the Ehrlich-Aberth method, Publications de l'Institut Mathématique 62 (1997) 141-149.
21. [21] M. S. Petković, L. V. Stefanović, On some parallel higher-order methods of Halley's type for finding multiple polynomial zeros in: G.V. Milovanovic, (Ed.), Proc. Internat. Conf. Numerical Methods and Approximation Theory, Faculty of Electronic Engineering, Niš 1987, pp. 329-337.
22. [22] M. S. Petković, S. Tričković, D. Herceg, On Euler-like methods for the simultaneous approximation of polynomial zeros, Japan J. Indust. Appl. Math., to appear.
23. [23] S. Smale, The fundamental theorem of algebra and complexity theory, Bull. Amer. Math. Soc. 4 (1981) 1-35.
24. [24] S. Smale, Newton's method estimates from data at one point. The Merging Disciplines: New Directions in Pure, Applied and Computational Mathematics, Springer, New York, 1986, pp. 185-196.
25. [25] D. Wang, F. Zhao, The theory of Smale's point estimation and its application, J. Comput. Appl. Math. 60 (1995) 253-269.
26. [26] X. Wang, D. Han, Scientia sinica A, (1989) 905-913.
27. [27] X. Wang, S. Zheng, A family of parallel and interval iterations for finding all roots of a polynomial simultaneously with rapid convergence I, J. Comput. Math. 1 (1984) 70-76.
28. [28] X. Wang, S. Zheng, A family of parallel and interval iterations for finding all roots of a polynomial simultaneously with rapid convergence (II), J. Comput. Math. 4 (1985) 433-444 (in Chinese).
29. [29] F. Zhao, D. Wang, The theory of Smale's point estimation and the convergence of Durand-Kerner program, Math. Numer. Sinica 15 (1993). 196-206 (in Chinese).