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Article

A New Family of High-Order Ehrlich-Type Iterative Methods

Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24 Tzar Asen, 4000 Plovdiv, Bulgaria
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Academic Editor: Theodore E. Simos
Mathematics 2021, 9(16), 1855; https://doi.org/10.3390/math9161855
Received: 19 July 2021 / Revised: 31 July 2021 / Accepted: 3 August 2021 / Published: 5 August 2021
(This article belongs to the Special Issue Numerical Analysis and Scientific Computing)
One of the famous third-order iterative methods for finding simultaneously all the zeros of a polynomial was introduced by Ehrlich in 1967. In this paper, we construct a new family of high-order iterative methods as a combination of Ehrlich’s iteration function and an arbitrary iteration function. We call these methods Ehrlich’s methods with correction. The paper provides a detailed local convergence analysis of presented iterative methods for a large class of iteration functions. As a consequence, we obtain two types of local convergence theorems as well as semilocal convergence theorems (with computer verifiable initial condition). As special cases of the main results, we study the convergence of several particular iterative methods. The paper ends with some experiments that show the applicability of our semilocal convergence theorems. View Full-Text
Keywords: iterative methods; simultaneous methods; Ehrlich method; polynomial zeros; accelerated convergence; local convergence; error estimates: semilocal convergence iterative methods; simultaneous methods; Ehrlich method; polynomial zeros; accelerated convergence; local convergence; error estimates: semilocal convergence
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MDPI and ACS Style

Proinov, P.D.; Vasileva, M.T. A New Family of High-Order Ehrlich-Type Iterative Methods. Mathematics 2021, 9, 1855. https://doi.org/10.3390/math9161855

AMA Style

Proinov PD, Vasileva MT. A New Family of High-Order Ehrlich-Type Iterative Methods. Mathematics. 2021; 9(16):1855. https://doi.org/10.3390/math9161855

Chicago/Turabian Style

Proinov, Petko D., and Maria T. Vasileva 2021. "A New Family of High-Order Ehrlich-Type Iterative Methods" Mathematics 9, no. 16: 1855. https://doi.org/10.3390/math9161855

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