Autor: |
Petko D. Proinov |
Jazyk: |
angličtina |
Rok vydání: |
2021 |
Předmět: |
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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 |
Externí odkaz: |
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