The convergence of Euler-like method for the simultaneous inclusion of polynomial zeros

Computers and Mathematics with Applications

Volumn 39, Issue 7-8, 2000, Pages 95-105

  Petkovic, M S ^a   Vranic, D V ^a  

^a Faculty of Electronic Engineering   (Serbia)

Author keywords

Convergence; Inclusion of zeros; Polynomial zeros; Simultaneous method

Indexed keywords

ALGORITHMS; CONVERGENCE OF NUMERICAL METHODS; POLES AND ZEROS; POLYNOMIALS; THEOREM PROVING;

EULER LIKE METHODS; POLYNOMIAL ZEROS; SIMULTANEOUS INCLUSION;

ITERATIVE METHODS;

EID: 0034174020     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0898-1221(00)00068-7     Document Type: Article

References (18)

1. M.S. Petkovic, Iterative Methods for Simultaneous Inclusion of Polynomial Zeros, Springer-Verlag, Berlin, (1989).
2. M.S. Petkovié, C. Carstensen and M. Trajkovié, Weierstrass formula and zero-finding methods, Numer. Math. 69, 353-372, (1995).
3. M.S. Petkovié and L.D. Petkovié, Complex Interval Arithmetic and its Applications, Wiley-VCH, Berlin, (1998).
4. M.S. Petkovié, S. Triékovié and D.J. Herceg, On Euler-like methods for the simultaneous approximation of polynomial zeros, Japan J. Indust. Appl. Math. 15, 295-315, (1998).
5. I. Gargantini and P. Henrici, Circular arithmetic and the determination of polynomial zeros, Numer. Math. 18, 305-320, (1972).
6. I. Gargantini, Parallel Laguerre iterations: Complex case, Numer. Math. 26, 317-323, (1976).
7. G. Alefeld and J. Herzberger, Introduction to Interval Computation, Academic Press, New York, (1983).
8. I. Gargantini, Further applications of circular arithmetic: Schroeder-like algorithms with error bounds for finding zeros of polynomials, SIAM J. Numer. Anal. 15, 497-510, (1978).
9. C. Carstensen and M.S. Petkovié, An improvement of Gargantini simultaneous inclusion method for polynomial roots by Schroeder's correction, Appl. Numer. Math. 25, 59-67, (1993).
10. M.S. Petkovié and C. Carstensen, Some improved inclusion methods for polynomial roots with Weierstrass' correction, Computers Math. Applic. 25 (3), 59-67, (1993).
11. M.S. Petkovié, Halley-like method with corrections for the inclusion of polynomial zeros, Computing 62, 69-88, (1999).
12. J.M. Ortega and W.O. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, (1970).
13. P. Henrici, Applied and Computational Complex Analysis, Volume I, John Wiley and Sons, New York, (1974).
14. M. Marden, Geometry of Polynomials, Mathematical surveys, Amer. Math. Soc., Providence, RI, (1985).
15. P. Kravanja, On Computing Zeros of Analytic Functions and Related Problems in Structured Numerical Linear Algebra, Ph.H. Thesis, University of Leuven, Leuven, (1999).
16. M.S. Petkovic, D.J. Herceg and S. Ilic, Point Estimation Theory and its Applications, Institute of Mathematics, Novi Sad, (1997).
17. B.T. Smith, Error bounds for zeros of a polynomial based upon Gerschgorin's theorem, J. Assoc. Comput. Mach. 17, 661-674, (1970).
18. D. Braess and K.P. Hadeler, Simultaneous inclusion of the zeros of a polynomial, Numer. Math. 21, 161-165, (1973).