Descripción del título
An Optimal Thirty-Second-Or...
Many multipoint iterative methods without memory for solving non-linear equations in one variable are found in the literature. In particular, there are methods that provide fourth-order, eighth-order or sixteenth-order convergence using only, respectively, three, four or five function evaluations per iteration step, thus supporting the Kung-Traub conjecture on the optimal order of convergence. This paper shows how to find optimal high order root-finding iterative methods by means of a general scheme based in weight functions. In particular, we explicitly give an optimal thirty-second-order iterative method; as long as we know, an iterative method with that order of convergence has not been described before. Finally, we give a conjecture about optimal order multipoint iterative methods with weights
Analítica
analitica Rebiun33853814 https://catalogo.rebiun.org/rebiun/record/Rebiun33853814 230721s2022 xx o 000 0 eng d https://dialnet.unirioja.es/servlet/oaiart?codigo=8307875 (Revista) ISSN 1575-5460 S9M oai:dialnet.unirioja.es:ART0001521736 https://dialnet.unirioja.es/oai/OAIHandler 11 DGCNT S9M S9M dc An Optimal Thirty-Second-Order Iterative Method for Solving Nonlinear Equations and a Conjecture electronic resource] 2022 application/pdf Open access content. Open access content star Many multipoint iterative methods without memory for solving non-linear equations in one variable are found in the literature. In particular, there are methods that provide fourth-order, eighth-order or sixteenth-order convergence using only, respectively, three, four or five function evaluations per iteration step, thus supporting the Kung-Traub conjecture on the optimal order of convergence. This paper shows how to find optimal high order root-finding iterative methods by means of a general scheme based in weight functions. In particular, we explicitly give an optimal thirty-second-order iterative method; as long as we know, an iterative method with that order of convergence has not been described before. Finally, we give a conjecture about optimal order multipoint iterative methods with weights LICENCIA DE USO: Los documentos a texto completo incluidos en Dialnet son de acceso libre y propiedad de sus autores y/o editores. Por tanto, cualquier acto de reproducción, distribución, comunicación pública y/o transformación total o parcial requiere el consentimiento expreso y escrito de aquéllos. Cualquier enlace al texto completo de estos documentos deberá hacerse a través de la URL oficial de éstos en Dialnet. Más información: https://dialnet.unirioja.es/info/derechosOAI | INTELLECTUAL PROPERTY RIGHTS STATEMENT: Full text documents hosted by Dialnet are protected by copyright and/or related rights. This digital object is accessible without charge, but its use is subject to the licensing conditions set by its authors or editors. Unless expressly stated otherwise in the licensing conditions, you are free to linking, browsing, printing and making a copy for your own personal purposes. All other acts of reproduction and communication to the public are subject to the licensing conditions expressed by editors and authors and require consent from them. Any link to this document should be made using its official URL in Dialnet. More info: https://dialnet.unirioja.es/info/derechosOAI English Multipoint iterative methods Simple root Order of convergence Kung and Traub's conjecture Basins of attraction text (article) Varona Malumbres, Juan Luis. cre Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 2, 2022 Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 2, 2022 Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 2, 2022