- -

An efficient iterative method based on two-stage splitting methods to solve weakly nonlinear systems

RiuNet: Repositorio Institucional de la Universidad Politécnica de Valencia

Compartir/Enviar a

Citas

Estadísticas

  • Estadisticas de Uso

An efficient iterative method based on two-stage splitting methods to solve weakly nonlinear systems

Mostrar el registro sencillo del ítem

Ficheros en el ítem

Thumbnail
Nombre: Amiri;Darvishi;Cordero ...
Tamaño: 293.6Kb
Formato: PDF
Descripción: Versión editorial
Abrir
dc.contributor.author Amiri, Abdolreza es_ES
dc.contributor.author Darvishi, Mohammad Taghi es_ES
dc.contributor.author Cordero Barbero, Alicia es_ES
dc.contributor.author Torregrosa Sánchez, Juan Ramón es_ES
dc.date.accessioned 2021-01-19T04:32:45Z
dc.date.available 2021-01-19T04:32:45Z
dc.date.issued 2019-09 es_ES
dc.identifier.uri http://hdl.handle.net/10251/159364
dc.description.abstract [EN] In this paper, an iterative method for solving large, sparse systems of weakly nonlinear equations is presented. This method is based on Hermitian/skew-Hermitian splitting (HSS) scheme. Under suitable assumptions, we establish the convergence theorem for this method. In addition, it is shown that any faster and less time-consuming two-stage splitting method that satisfies the convergence theorem can be replaced instead of the HSS inner iterations. Numerical results, such as CPU time, show the robustness of our new method. This method is easy, fast and convenient with an accurate solution. es_ES
dc.description.sponsorship The third and fourth authors have been partially supported by the Spanish Ministerio de Ciencia, Innovacion y Universidades PGC2018-095896-B-C22 and Generalitat Valenciana PROMETEO/2016/089. es_ES
dc.language Inglés es_ES
dc.publisher MDPI AG es_ES
dc.relation.ispartof Mathematics es_ES
dc.rights Reconocimiento (by) es_ES
dc.subject System of nonlinear equations es_ES
dc.subject Newton method es_ES
dc.subject Newton-HSS method es_ES
dc.subject Nonlinear HSS-like method es_ES
dc.subject Picard-HSS method es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title An efficient iterative method based on two-stage splitting methods to solve weakly nonlinear systems es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.3390/math7090815 es_ES
dc.relation.projectID info:eu-repo/grantAgreement/GVA//PROMETEO%2F2016%2F089/ES/Resolución de ecuaciones y sistemas no lineales mediante técnicas iterativas: análisis dinámico y aplicaciones/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PGC2018-095896-B-C22/ES/DISEÑO, ANALISIS Y ESTABILIDAD DE PROCESOS ITERATIVOS APLICADOS A LAS ECUACIONES INTEGRALES Y MATRICIALES Y A LA COMUNICACION AEROESPACIAL/ es_ES
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada es_ES
dc.description.bibliographicCitation Amiri, A.; Darvishi, MT.; Cordero Barbero, A.; Torregrosa Sánchez, JR. (2019). An efficient iterative method based on two-stage splitting methods to solve weakly nonlinear systems. Mathematics. 7(9):1-17. https://doi.org/10.3390/math7090815 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://doi.org/10.3390/math7090815 es_ES
dc.description.upvformatpinicio 1 es_ES
dc.description.upvformatpfin 17 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 7 es_ES
dc.description.issue 9 es_ES
dc.identifier.eissn 2227-7390 es_ES
dc.relation.pasarela S\393515 es_ES
dc.contributor.funder Generalitat Valenciana es_ES
dc.contributor.funder Agencia Estatal de Investigación es_ES
dc.description.references Shen, W., & Li, C. (2009). Kantorovich-type convergence criterion for inexact Newton methods. Applied Numerical Mathematics, 59(7), 1599-1611. doi:10.1016/j.apnum.2008.11.002 es_ES
dc.description.references An, H.-B., & Bai, Z.-Z. (2007). A globally convergent Newton-GMRES method for large sparse systems of nonlinear equations. Applied Numerical Mathematics, 57(3), 235-252. doi:10.1016/j.apnum.2006.02.007 es_ES
dc.description.references Eisenstat, S. C., & Walker, H. F. (1994). Globally Convergent Inexact Newton Methods. SIAM Journal on Optimization, 4(2), 393-422. doi:10.1137/0804022 es_ES
dc.description.references Gomes-Ruggiero, M. A., Lopes, V. L. R., & Toledo-Benavides, J. V. (2007). A globally convergent inexact Newton method with a new choice for the forcing term. Annals of Operations Research, 157(1), 193-205. doi:10.1007/s10479-007-0196-y es_ES
dc.description.references Bai, Z. (1997). Numerical Algorithms, 14(4), 295-319. doi:10.1023/a:1019125332723 es_ES
dc.description.references Axelsson, O., Bai, Z.-Z., & Qiu, S.-X. (2004). A Class of Nested Iteration Schemes for Linear Systems with a Coefficient Matrix with a Dominant Positive Definite Symmetric Part. Numerical Algorithms, 35(2-4), 351-372. doi:10.1023/b:numa.0000021766.70028.66 es_ES
dc.description.references Bai, Z.-Z., Golub, G. H., & Ng, M. K. (2003). Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive Definite Linear Systems. SIAM Journal on Matrix Analysis and Applications, 24(3), 603-626. doi:10.1137/s0895479801395458 es_ES
dc.description.references Li, L., Huang, T.-Z., & Liu, X.-P. (2007). Asymmetric Hermitian and skew-Hermitian splitting methods for positive definite linear systems. Computers & Mathematics with Applications, 54(1), 147-159. doi:10.1016/j.camwa.2006.12.024 es_ES
dc.description.references Bai, Z.-Z., & Yang, X. (2009). On HSS-based iteration methods for weakly nonlinear systems. Applied Numerical Mathematics, 59(12), 2923-2936. doi:10.1016/j.apnum.2009.06.005 es_ES
dc.description.references Bai, Z.-Z., Migallón, V., Penadés, J., & Szyld, D. B. (1999). Block and asynchronous two-stage methods for mildly nonlinear systems. Numerische Mathematik, 82(1), 1-20. doi:10.1007/s002110050409 es_ES
dc.description.references Zhu, M.-Z., & Zhang, G.-F. (2011). On CSCS-based iteration methods for Toeplitz system of weakly nonlinear equations. Journal of Computational and Applied Mathematics, 235(17), 5095-5104. doi:10.1016/j.cam.2011.04.038 es_ES
dc.description.references Guo, Z.-Z. B. and X.-P. (2010). On Newton-HSS Methods for Systems of Nonliear Equations with Positive-Definite Jacobian Matrices. Journal of Computational Mathematics, 28(2), 235-260. doi:10.4208/jcm.2009.10-m2836 es_ES
dc.description.references Cao, Y., Wei Tan, W.-, & Jiang, M.-Q. (2012). A generalization of the positive-definite and skew-Hermitian splitting iteration. Numerical Algebra, Control & Optimization, 2(4), 811-821. doi:10.3934/naco.2012.2.811 es_ES
dc.description.references Bai, Z.-Z., Golub, G. H., & Ng, M. K. (2008). On inexact hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems. Linear Algebra and its Applications, 428(2-3), 413-440. doi:10.1016/j.laa.2007.02.018 es_ES
dc.description.references Bai, Z.-Z., Golub, G. H., Lu, L.-Z., & Yin, J.-F. (2005). Block Triangular and Skew-Hermitian Splitting Methods for Positive-Definite Linear Systems. SIAM Journal on Scientific Computing, 26(3), 844-863. doi:10.1137/s1064827503428114 es_ES


Este ítem aparece en la(s) siguiente(s) colección(ones)

Mostrar el registro sencillo del ítem