On the Convergence of a New Family of Multi-Point Ehrlich-Type Iterative Methods for Polynomial Zeros

In this paper, we construct and study a new family of multi-point Ehrlich-type iterative methods for approximating all the zeros of a uni-variate polynomial simultaneously. The first member of this family is the two-point Ehrlich-type iterative method introduced and studied by Trićković and Petković...

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Main Authors:	Petko D. Proinov, Milena D. Petkova
Format:	Article
Language:	English
Published:	MDPI AG 2021-07-01
Series:	Mathematics
Subjects:	multi-point iterative methods iteration functions polynomial zeros local convergence error estimates semilocal convergence
Online Access:	https://www.mdpi.com/2227-7390/9/14/1640

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spelling	doaj-d0c0c6a21c8341059dc458f97938ec5e2021-07-23T13:52:27ZengMDPI AGMathematics2227-73902021-07-0191640164010.3390/math9141640On the Convergence of a New Family of Multi-Point Ehrlich-Type Iterative Methods for Polynomial ZerosPetko D. Proinov0Milena D. Petkova1Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24 Tzar Asen, 4000 Plovdiv, BulgariaFaculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24 Tzar Asen, 4000 Plovdiv, BulgariaIn this paper, we construct and study a new family of multi-point Ehrlich-type iterative methods for approximating all the zeros of a uni-variate polynomial simultaneously. The first member of this family is the two-point Ehrlich-type iterative method introduced and studied by Trićković and Petković in 1999. The main purpose of the paper is to provide local and semilocal convergence analysis of the multi-point Ehrlich-type methods. Our local convergence theorem is obtained by an approach that was introduced by the authors in 2020. Two numerical examples are presented to show the applicability of our semilocal convergence theorem.https://www.mdpi.com/2227-7390/9/14/1640multi-point iterative methodsiteration functionspolynomial zeroslocal convergenceerror estimatessemilocal convergence
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Petko D. Proinov Milena D. Petkova
spellingShingle	Petko D. Proinov Milena D. Petkova On the Convergence of a New Family of Multi-Point Ehrlich-Type Iterative Methods for Polynomial Zeros Mathematics multi-point iterative methods iteration functions polynomial zeros local convergence error estimates semilocal convergence
author_facet	Petko D. Proinov Milena D. Petkova
author_sort	Petko D. Proinov
title	On the Convergence of a New Family of Multi-Point Ehrlich-Type Iterative Methods for Polynomial Zeros
title_short	On the Convergence of a New Family of Multi-Point Ehrlich-Type Iterative Methods for Polynomial Zeros
title_full	On the Convergence of a New Family of Multi-Point Ehrlich-Type Iterative Methods for Polynomial Zeros
title_fullStr	On the Convergence of a New Family of Multi-Point Ehrlich-Type Iterative Methods for Polynomial Zeros
title_full_unstemmed	On the Convergence of a New Family of Multi-Point Ehrlich-Type Iterative Methods for Polynomial Zeros
title_sort	on the convergence of a new family of multi-point ehrlich-type iterative methods for polynomial zeros
publisher	MDPI AG
series	Mathematics
issn	2227-7390
publishDate	2021-07-01
description	In this paper, we construct and study a new family of multi-point Ehrlich-type iterative methods for approximating all the zeros of a uni-variate polynomial simultaneously. The first member of this family is the two-point Ehrlich-type iterative method introduced and studied by Trićković and Petković in 1999. The main purpose of the paper is to provide local and semilocal convergence analysis of the multi-point Ehrlich-type methods. Our local convergence theorem is obtained by an approach that was introduced by the authors in 2020. Two numerical examples are presented to show the applicability of our semilocal convergence theorem.
topic	multi-point iterative methods iteration functions polynomial zeros local convergence error estimates semilocal convergence
url	https://www.mdpi.com/2227-7390/9/14/1640
work_keys_str_mv	AT petkodproinov ontheconvergenceofanewfamilyofmultipointehrlichtypeiterativemethodsforpolynomialzeros AT milenadpetkova ontheconvergenceofanewfamilyofmultipointehrlichtypeiterativemethodsforpolynomialzeros
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On the Convergence of a New Family of Multi-Point Ehrlich-Type Iterative Methods for Polynomial Zeros

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