A family of two-point methods with memory for solving nonlinear equations

Autor:	Jovana Dzunic, D Ljiljana Petkovic, S Miodrag Petkovic
Rok vydání:	2011
Předmět:	Mathematical optimization Matrix-free methods Iterative method Applied Mathematics Function (mathematics) Nonlinear system Rate of convergence Convergence (routing) Discrete Mathematics and Combinatorics Applied mathematics Point (geometry) Analysis Mathematics Free parameter
Zdroj:	Applicable Analysis and Discrete Mathematics. 5:298-317
ISSN:	2406-100X 1452-8630
DOI:	10.2298/aadm110905021p
Popis:	An efficient family of two-point derivative free methods with memory for solving nonlinear equations is presented. It is proved that the convergence order of the proposed family is increased from 4 to at least 2 + ?6 ? 4.45, 5, 1/2 (5 + ?33) ? 5.37 and 6, depending on the accelerating technique. The increase of convergence order is attained using a suitable accelerating technique by varying a free parameter in each iteration. The improvement of convergence rate is achieved without any additional function evaluations meaning that the proposed methods with memory are very efficient. Moreover, the presented methods are more efficient than all existing methods known in literature in the class of two-point methods and three-point methods of optimal order eight. Numerical examples and the comparison with the existing two-point methods are included to confirm theoretical results and high computational efficiency. 2010 Mathematics Subject Classification. 65H05
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::622e4d4f7e1a5a240a52287c3895678a https://doi.org/10.2298/aadm110905021p Zobrazit plný text záznamu Plný text ve formátu PDF