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

Unified convergence analysis for Picard iteration in n-dimensional vector spaces 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). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Calcolo Springer Journals

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

Calcolo , Volume 55 (1) – Feb 9, 2018

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer-Verlag Italia S.r.l., part of Springer Nature
Subject
Mathematics; Numerical Analysis; Theory of Computation
ISSN
0008-0624
eISSN
1126-5434
D.O.I.
10.1007/s10092-018-0251-x
Publisher site
See Article on Publisher Site

Abstract

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).

Journal

CalcoloSpringer Journals

Published: Feb 9, 2018

References

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