nach oben

BIT Numerical Mathematics

Erschienen in:

01.06.2016

Accelerated SOR-like method for augmented linear systems

verfasst von: Patrick Njue Njeru, Xue-Ping Guo

Erschienen in: BIT Numerical Mathematics | Ausgabe 2/2016

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

By accelerating the SOR-like method by two parameters alpha and omega, we propose an accelerated SOR-like (ASOR) method for solving the augmented linear systems. The convergence of the ASOR method is discussed under suitable restrictions on the iteration parameters alpha and omega, and the experimental optimal values of the iteration parameters are determined. Numerical results are presented to show the efficiency of the ASOR method when the iteration parameters alpha and omega are suitably chosen.

Vorheriger Artikel The generalized HSS method with a flexible shift-parameter for non-Hermitian positive definite linear systems

Nächster Artikel Computational fluid dynamics for nematic liquid crystals

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Bai, Z.-Z.: Structured preconditioners for nonsingular matrices of block two-by-two structures. Math. Comput. 75, 791–815 (2006)MathSciNetCrossRefMATH

Bai, Z.-Z.: Optimal parameters in the HSS-like methods for saddle-point problems. Numer. Linear Algebra Appl. 16, 447–479 (2009)MathSciNetCrossRefMATH

Bai, Z.-Z., Golub, G.H.: Accelerated Hermitian and skew-Hermitian splitting iteration methods for saddle point problems. IMA J. Numer. Anal. 27, 1–23 (2007)MathSciNetCrossRefMATH

Bai, Z.-Z., Golub, G.H., Li, C.-K.: Convergence properties of preconditioned Hermitian and skew-Hermitian splitting method for non-Hermitian positive-definite linear systems. Math. Comput. 76, 287–298 (2007)MathSciNetCrossRefMATH

Bai, Z.-Z., Golub, G.H., Ng, M.K.: Hermitian and skew-Hermitian splitting method for non-Hermitian positive-definite linear systems. SIAM J. Matrix Anal. Appl. 24, 603–626 (2003)MathSciNetCrossRefMATH

Bai, Z.-Z., Golub, G.H., Pan, J.-Y.: Preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite linear systems. Numer. Math. 98, 1–32 (2004)MathSciNetCrossRefMATH

Bai, Z.-Z., Parlett, B.N., Wang, Z.-Q.: On generalized successive overrelaxation methods for augmented linear systems. Numer. Math. 102, 1–38 (2005)MathSciNetCrossRefMATH

Bai, Z.-Z., Wang, Z.-Q.: On parameterized inexact Uzawa methods for generalized saddle point problems. Linear Algebra Appl. 428, 2900–2932 (2008)MathSciNetCrossRefMATH

Benzi, M., Golub, G.H.: A preconditioner for generalized saddle point problems. SIAM J. Matrix Anal. Appl. 26, 20–41 (2004)MathSciNetCrossRefMATH

10.

Chao, Z., Zhang, N., Lu, Y.-Z.: Optimal parameters of the generalized symmetric SOR method for augmented systems. J. Comput. Appl. Math. 266, 52–60 (2014)MathSciNetCrossRefMATH

11.

Darvishi, M.T., Hessari, P.: A modified symmetric successive overrelaxation method for augmented systems. Comput. Math. Appl. 61, 3128–3135 (2011)MathSciNetCrossRefMATH

12.

Darvishi, M.T., Hessari, P.: Symmetric SOR method for augmented systems. Appl. Math. Comput. 183, 409–415 (2006)MathSciNetMATH

13.

Elman, H.C., Silvester, D.J.: Fast nonsymmetric iterations and preconditioning for Navier–Stokes equations. SIAM J. Sci. Comput. 17, 33–46 (1996)MathSciNetCrossRefMATH

14.

Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: With Applications in Incompressible Fluid Dynamics. Oxford University Press, New York (2005)MATH

15.

Fischer, B., Ramage, A., Silvester, D.J., Wathen, A.J.: Minimum residual methods for augmented systems. BIT 38, 527–543 (1998)MathSciNetCrossRefMATH

16.

Golub, G.H., Wu, X., Yuan, J.-Y.: SOR-like method for augmented systems. BIT Numer. Math. 41, 71–85 (2001)MathSciNetCrossRefMATH

17.

Hadjidimos, A.: Successive overrelaxation (SOR) and related methods. J. Comput. Appl. Math. 123, 177–199 (2000)MathSciNetCrossRefMATH

18.

Li, C.-J., Li, B.-J., Evans, D.J.: A generalized successive overrelaxation method for the least squares problems. BIT 38, 347–356 (1998)MathSciNetCrossRefMATH

19.

Li, C.-J., Li, Z., Evans, D.J., Zhang, T.: A note on an SOR-like method for augmented systems. IMA J. Numer. Anal. 23, 581–592 (2003)MathSciNetCrossRefMATH

20.

Martins, M.M., Yousif, W., Santos, J.L.: A variant of the AOR method for augmented systems. Math. Comput. 81, 399–417 (2012)MathSciNetCrossRefMATH

21.

Salkuyeh, D.K., Shamsi, S., Sadeghi, A.: An improved symmetric SOR iterative method for augmented systems. Tamkang J. Math. 43, 479–490 (2012)MathSciNetMATH

22.

Santos, C.H., Sival, B.P., Yuan, J.-Y.: Block SOR method for rank deficient least squares problems. Comput. Appl. Math. 100, 1–9 (1998)MathSciNetCrossRefMATH

23.

Shao, X.-H., Zheng, L., Li, C.-J.: Modified SOR-like method for augmented systems. Int. J. Comput. Math. 84, 1653–1662 (2007)MathSciNetCrossRefMATH

24.

Wang, X.-M.: Convergence for a general form of the GAOR method and its application to the MSOR method. Linear Algebra Appl. 196, 105–123 (1994)MathSciNetCrossRefMATH

25.

Wright, S.: Stability of augmented systems factorizations in interior-point methods. SIAM Matrix Anal. Appl. 18, 191–222 (1997)CrossRefMATH

26.

Wu, S.-L., Huang, T.-Z., Zhao, X.-L.: A modified SSOR iterative method for augmented systems. J. Comput. Appl. Math. 228, 424–433 (2009)MathSciNetCrossRefMATH

27.

Yuan, J.-Y.: Numerical methods for generalized least squares problems. Comput. Appl. Math. 66, 571–584 (1996)MathSciNetCrossRefMATH

28.

Young, D.M.: Iterative Solutions of Large Linear Systems. Academic Press, New York (1971)

29.

Zhang, G.-F., Lu, Q.-H.: On generalized symmetric SOR method for augmented systems. J. Comput. Appl. Math. 219, 51–58 (2008)MathSciNetCrossRefMATH

Titel: Accelerated SOR-like method for augmented linear systems
verfasst von: Patrick Njue Njeru
Xue-Ping Guo
Publikationsdatum: 01.06.2016
Verlag: Springer Netherlands
Erschienen in: BIT Numerical Mathematics / Ausgabe 2/2016
Print ISSN: 0006-3835
Elektronische ISSN: 1572-9125
DOI: https://doi.org/10.1007/s10543-015-0571-z

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft"

Springer Professional "Technik"

Springer Professional "Wirtschaft+Technik"

Weitere Artikel der Ausgabe 2/2016

Simple floating-point filters for the two-dimensional orientation problem

Structural-algebraic regularization for coupled systems of DAEs

A simplified HSS preconditioner for generalized saddle point problems

Monotone finite point method for non-equilibrium radiation diffusion equations

Nonautonomous systems with transversal homoclinic structures under discretization

A triple-parameter modified SSOR method for solving singular saddle point problems

Premium Partner