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

被引：0
|
作者：
Petko D. Proinov
机构：
[1] University of Plovdiv Paisii Hilendarski,Faculty of Mathematics and Informatics
来源：
Calcolo | 2018年 / 55卷
关键词：
Picard iteration; Successive approximations; Local convergence; Semilocal convergence; Error estimates; Newton method; 65J15; 47J25; 47H10; 54H25; 65H05;
D O I：
暂无
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学科分类号：
摘要：
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).
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