- -

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

RiuNet: Institutional repository of the Polithecnic University of Valencia

Share/Send to

Cited by

Statistics

  • Estadisticas de Uso

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

Show full item record

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

Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/159364

Files in this item

Item Metadata

Title: An efficient iterative method based on two-stage splitting methods to solve weakly nonlinear systems
Author: Amiri, Abdolreza Darvishi, Mohammad Taghi Cordero Barbero, Alicia Torregrosa Sánchez, Juan Ramón
UPV Unit: Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
Issued date:
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 ...[+]
Subjects: System of nonlinear equations , Newton method , Newton-HSS method , Nonlinear HSS-like method , Picard-HSS method
Copyrigths: Reconocimiento (by)
Source:
Mathematics. (eissn: 2227-7390 )
DOI: 10.3390/math7090815
Publisher:
MDPI AG
Publisher version: https://doi.org/10.3390/math7090815
Project ID:
info:eu-repo/grantAgreement/GVA//PROMETEO%2F2016%2F089/ES/Resolución de ecuaciones y sistemas no lineales mediante técnicas iterativas: análisis dinámico y aplicaciones/
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/
Thanks:
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.
Type: Artículo

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

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

Eisenstat, S. C., & Walker, H. F. (1994). Globally Convergent Inexact Newton Methods. SIAM Journal on Optimization, 4(2), 393-422. doi:10.1137/0804022 [+]
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

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

Eisenstat, S. C., & Walker, H. F. (1994). Globally Convergent Inexact Newton Methods. SIAM Journal on Optimization, 4(2), 393-422. doi:10.1137/0804022

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

Bai, Z. (1997). Numerical Algorithms, 14(4), 295-319. doi:10.1023/a:1019125332723

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

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

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

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

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

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

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

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

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

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

[-]

recommendations

 

This item appears in the following Collection(s)

Show full item record