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

Petko D. Proinov and Maria T. Vasileva
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Petko D. Proinov: Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24 Tzar Asen, 4000 Plovdiv, Bulgaria
Maria T. Vasileva: Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24 Tzar Asen, 4000 Plovdiv, Bulgaria

Mathematics, 2021, vol. 9, issue 16, 1-25

Abstract: 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.

Keywords: iterative methods; simultaneous methods; Ehrlich method; polynomial zeros; accelerated convergence; local convergence; error estimates: semilocal convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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