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Unified convergence analysis for Picard iteration in n -dimensional vector spaces (2018)

Springer

In: CALCOLO

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Publication Date: 2018-03-06

Description: In this paper, we provide three types of general convergence theorems for Picard iteration in n -dimensional vector spaces over a valued field. These theorems can be used as tools to study the convergence of some particular Picard-type iterative methods. As an application, we present a new semilocal convergence theorem for the one-dimensional Newton method for approximating all the zeros of a polynomial simultaneously. This result improves in several directions the previous one given by Batra (BIT Numer Math 42:467–476, 2002 ).

Print ISSN: 0008-0624

Electronic ISSN: 1126-5434

Topics: Mathematics

Published by Springer

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