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

✍ Scribed by M.S. Petković; L.D. Petković; J. Džunić

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
397 KB
Volume
59
Category
Article
ISSN
0898-1221

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✦ Synopsis

a b s t r a c t 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.

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