Howk, CL.; Hueso, J.; Martínez Molada, E.; Teruel-Ferragud, C. (2018). A class of efficient high-order iterative methods with memory for nonlinear equations and their dynamics. Mathematical Methods in the Applied Sciences. 41(17):7263-7282. https://doi.org/10.1002/mma.4821
Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/125220
Title:
|
A class of efficient high-order iterative methods with memory for nonlinear equations and their dynamics
|
Author:
|
Howk, Cory L.
Hueso, J.L.
Martínez Molada, Eulalia
Teruel-Ferragud, Carles
|
UPV Unit:
|
Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
|
Issued date:
|
|
Abstract:
|
[EN] In this paper we obtain some theoretical results about iterative methods with memory for nonlinear equations. The class of algorithms we consider focus on incorporating memory without increasing the computational cost ...[+]
[EN] In this paper we obtain some theoretical results about iterative methods with memory for nonlinear equations. The class of algorithms we consider focus on incorporating memory without increasing the computational cost of the algorithm. This class uses for the predictor step of each iteration a quantity that has already been calculated in the previous iteration, typically the quantity governing the slope from the previous corrector step. In this way we do not introduce any extra computation, and more importantly, we avoid new function evaluations, allowing us to obtain high-order iterative methods in a simple way. A specific class of methods of this type is introduced, and we prove the convergence order is 2(n) + 2(n-2) with n + 1 function evaluations. An exhaustive efficiency study is performed to show the competitiveness of these methods. Finally, we test some specific examples and explore the effect that this predictor may have on the convergence set by setting a dynamical study.
[-]
|
Subjects:
|
Convergence rate
,
Dynamics
,
Efficiency
,
Iterative methods with memory
,
Kung-Traub conjecture
|
Copyrigths:
|
Reserva de todos los derechos
|
Source:
|
Mathematical Methods in the Applied Sciences. (issn:
0170-4214
)
|
DOI:
|
10.1002/mma.4821
|
Publisher:
|
John Wiley & Sons
|
Publisher version:
|
http://doi.org/10.1002/mma.4821
|
Conference name:
|
17th International Conference on Computational and Mathematical Methods in Science and Engineering (CMMSE 2017)
|
Conference place:
|
Rota, Spain
|
Conference date:
|
Julio 04-08,2017
|
Project ID:
|
info:eu-repo/grantAgreement/MINECO//MTM2014-52016-C2-2-P/ES/DISEÑO DE METODOS ITERATIVOS EFICIENTES PARA RESOLVER PROBLEMAS NO LINEALES: CONVERGENCIA, COMPORTAMIENTO DINAMICO Y APLICACIONES. ECUACIONES MATRICIALES./
info:eu-repo/grantAgreement/GVA//PROMETEO%2F2016%2F089/ES/Resolución de ecuaciones y sistemas no lineales mediante técnicas iterativas: análisis dinámico y aplicaciones/
|
Thanks:
|
Ministerio de Economia y Competitividad de Espana, Grant/Award Number: MTM2014-52016-C2-2-P; Generalitat Valenciana Prometeo, Grant/Award Number: /2016/089
|
Type:
|
Artículo
Comunicación en congreso
|