Two Classes of Iteration Functions and Q-Convergence of Two Iterative Methods for Polynomial Zeros

Autor: Petko D. Proinov
Jazyk: angličtina
Rok vydání: 2021
Předmět:
Zdroj: Symmetry, Vol 13, Iss 3, p 371 (2021)
Druh dokumentu: article
ISSN: 2073-8994
DOI: 10.3390/sym13030371
Popis: In this work, two broad classes of iteration functions in n-dimensional vector spaces are introduced. They are called iteration functions of the first and second kind at a fixed point of the corresponding iteration function. Two general local convergence theorems are presented for Picard-type iterative methods with high Q-order of convergence. In particular, it is shown that if an iterative method is generated by an iteration function of first or second kind, then it is Q-convergent under each initial approximation that is sufficiently close to the fixed point. As an application, a detailed local convergence analysis of two fourth-order iterative methods is provided for finding all zeros of a polynomial simultaneously. The new results improve the previous ones for these methods in several directions.
Databáze: Directory of Open Access Journals
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