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