Accelerating generators of iterative methods for finding multiple roots of nonlinear equations

Authors:
M. S. Petković;L. D. Petković;J. Dunić
Affiliations:
Faculty of Electronic Engineering, Department of Mathematics, University of Niš, 18000 Niš, Serbia;Faculty of Mechanical Engineering, Department of Mathematics, University of Niš, 18000 Niš, Serbia;Faculty of Electronic Engineering, Department of Mathematics, University of Niš, 18000 Niš, Serbia
Venue:
Computers & Mathematics with Applications
Year:
2010

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Abstract

Two accelerating generators that produce iterative root-finding methods of arbitrary order of convergence are presented. Primary attention is paid to algorithms for finding multiple roots of nonlinear functions and, in particular, of algebraic polynomials. First, two classes of algorithms for solving nonlinear equations are studied: those with a known order of multiplicity and others with no information on multiplicity. We also demonstrate the acceleration of iterative methods for the simultaneous approximations of multiple roots of algebraic polynomials. A discussion about the computational efficiency of the root-solvers considered and three numerical examples are given.