Skip to main content

A Class of New Generalized AOR Method for Augmented Systems

  • Conference paper
Advances in Neural Networks – ISNN 2011 (ISNN 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6675))

Included in the following conference series:

Abstract

In this paper, a class of new generalized AOR (GAOR) method with four parameters for augmented systems is established. This new method includes the SOR-Like method as a special case. The convergence of the new GAOR method for augmented systems is also studied. Numerical result is used to illustrate the efficiency of this new GAOR method.

The project Supported by ‘QingLan’ Talent Engineering Funds and SRF(TSA0928) by Tianshui Normal University.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Chun, C., Ham, Y.M.: Some sixth-order variants of Ostrowski root-finding methods. Appl. Math. Comput. 193, 389–394 (2007)

    MathSciNet  MATH  Google Scholar 

  2. Arioli, M., Duff, I.S., de Rijk, P.P.M.: On the augmented system approach to sparse least squares problems. Numer. Math. 55, 667–684 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bai, Z.Z., Parlett, B.N., Wang, Z.-Q.: On generalized successive overrelaxation methods for augmented linear systems. Numerische Mathematik (2005)

    Google Scholar 

  4. Darvishi, M.T., Hessari, P.: On convergence of the generalized AOR method for linear systems with diagonally dominant coefficient matrices. Appl. Math. Computk 176, 128–133 (2006)

    MathSciNet  MATH  Google Scholar 

  5. Darvishi, M.T., Hessari, P.: Symmetrci SOR method for augmented systems. Appl. Math. Comput. (2006)

    Google Scholar 

  6. Darvishi, M.T., Khosro-Aghdam, R.: Symmetric successive overrelaxation methods for rank deficient linear systems. Appl. Math. Comput. 173, 404–420 (2006)

    MathSciNet  MATH  Google Scholar 

  7. Elman, H., Golub, G.H.: Symmetric Inexact and precondioned Uzawa algorithms for saddle point problems. SIAM J. Numer. Anal. 31, 1645–1661 (1994)

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  10. Golub, G.H., Wu, X., Yuan, J.Y.: SOR-like methods for augmented systems. BIT 55, 71–85 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  11. Hadjidimos, A., Yeyios, A.: The symmetric accelerated overrelaxation (SAOR) method. Math. Comput. Simulat. XXIV, 72–76 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  12. Hu, Q.Y., Zou, J.: An iterative method with variable relaxation parameters for saddle-point problems. Math. SIMA J. Matrix Anal. Appl. 23, 317–338 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  13. Santos, G.H., Silva, B.P.B., Yuan, J.Y.: Block SOR methods for rank deficient least squares problems. J. Comput. Appl. Math. 75 (1998)

    Google Scholar 

  14. Santos, G.H., Yuan, J.Y.: Preconditioned conjugate gradient methods for rank deficient least squares problems. Int. J. Comput. Math. 75 (1999)

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  16. Young, D.M.: Iteratice solution for large linear systems. Academic Press, New York (1971)

    Google Scholar 

  17. Yuan, J.Y., Iusem, A.N.: Preconditioned conjugate gradient methods for generalized least squares problems. Comput. Appl. Math. 71, 287–297 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  18. Zhang, G.F., Lu, Q.H.: On generalized SSOR method for augmented systems, Accepted manuscript. Accepted manuscript. J. Comput. Appl. Math. (2007)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Zhang, Yx., Ding, Hf., He, Ws., Wang, Sf. (2011). A Class of New Generalized AOR Method for Augmented Systems. In: Liu, D., Zhang, H., Polycarpou, M., Alippi, C., He, H. (eds) Advances in Neural Networks – ISNN 2011. ISNN 2011. Lecture Notes in Computer Science, vol 6675. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21105-8_20

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-21105-8_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21104-1

  • Online ISBN: 978-3-642-21105-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics