Derivative Free Inclusion Methods for Polynomial Zeros

Authors:
M. S. Petković;D. Milošević
Affiliations:
Faculty of Electronic Engineering, University of Niš, P. O. Box 73, 18 000, Niš, Serbia and Montenegro;Faculty of Electronic Engineering, University of Niš, P. O. Box 73, 18 000, Niš, Serbia and Montenegro
Venue:
Computing - Editorial: Special issue on GAMM – Workshop on Guaranteed Error-bounds for the Solution of Nonlinear Problems in Applied Mathematics
Year:
2005

Citing 5
Cited 0

On Halley-like algorithms for simultaneous approximation of polynomial complex zeros

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On iteration methods without derivatives for the simultaneous determination of polynomial zeros

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On an accelerating quasi-newton circular iteration

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Iterative solution of nonlinear equations in several variables

Iterative solution of nonlinear equations in several variables

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Abstract

Two iterative methods for the simultaneous inclusion of complex zeros of a polynomial are presented. Both methods are realized in circular interval arithmetic and do not use polynomial derivatives. The first method of the fourth order is composed as a combination of interval methods with the order of convergence two and three. The second method is constructed using double application of the inclusion method of Weierstrass’ type in serial mode. It is shown that its R-order of convergence is bounded below by the spectral radius of the corresponding matrix. Numerical examples illustrate the convergence rate of the presented methods