Skip to main content
SpringerLink
Log in

The Construction of the Interpolation Operator with I L U Decomposition for Algebraic Positive Definite Systems

  • Chapter
Incomplete Decomposition (ILU) — Algorithms, Theory, and Applications

Part of the book series: Notes on Numerical Fluid Mechanics (NNFM) ((NNFM,volume 29))

  • 26 Accesses

Summary

We present in this paper two results concerning the convergence of the teo-grid algebraic algorithm for arbitrary symmetric systems of linear equations which are also positive definite.Ue obtain these results using a special construction of the interpolation operator based on Gaussian elimination on a sub-matrix of the original system matrix.At the end of the paper we make also some remarks concerning the symmetric indefinite systems.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 49.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.99
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. Brandt, A. : “Algebraic multigrid theory: the symmetric case”,Preprint ,weizmann Inst.of Science,Rehovot,Israel, 1983 .

    Google Scholar 

  2. Greenbaum,A. : “Analysis of a multigrid method as an iterative technique for salving linear systems”,SIAM 3. Num. Anal.,vol. 21,nr.3, (1984),pp.473 to 485 .

    Article  MATH  MathSciNet  Google Scholar 

  3. Hackbusch, W. : “Multigrid methods and applications”,Springer-Verlag Berlin (1985).

    Google Scholar 

  4. Juncu, Gh.,Popa, C. : “Introduction to the multigrid method”(in romanianj,Ed. Tehnica,Bucharest(1991) .

    Google Scholar 

  5. Meijerink, J.A.,van der Vorst, H.A. : “An iterative solution method for linear systems of which the coefficient matrix is a symmetric M—matrix”,math, of Comp.,vol.31,nr.137(1977),pp.148 to 162 .

    MATH  Google Scholar 

  6. Nicolaides, R.A. : “On multigrid convergence in the indefinite case” Report ICASE—VA,nr. 23655,NASA(1977) .

    Google Scholar 

  7. Papa, C. : “I L U decompesitien for coarse grid correction step on algebraic multigrid”,in Multigrid Methods II : Special Topics and Applications,G M D Studien,nr.l89(l99l) .

    Google Scholar 

  8. Popa, C. :On the smoothing properties of S D R relaxation for algebraic “multigrid method”,Studii si Cerc. Matem.,vol.5(l989) •

    Google Scholar 

  9. Popa, C. : “Algebraic multigrid for approximate solutions of symmetric systems,”,to appear in Proceed, of the 4-th Conf. on Math, and Applications,Timisoara,november 1991 .

    Google Scholar 

  10. J Ruge, J.,Stuben. K. : “Algebraic multigrid (AMG)”,Arbeitspapiereder G M D,nr. 210 (1986) .

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Constanta, Bd.Mamaia,nr.124, Constanta, 8700, Romania

    Constantin Popa

Authors
  1. Constantin Popa
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institut für Informatik und Praktische Mathematik, Christian-Albrechts-Universität Kiel, Olshausenstr. 40, W - 2300, Kiel 1, Deutschland

    Wolfgang Hackbusch

  2. IWR, Universität Heidelberg, Im Neuenheimer Feld 368, W - 6900, Heidelberg, Deutschland

    Gabriel Wittum

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden

About this chapter

Cite this chapter

Popa, C. (1993). The Construction of the Interpolation Operator with I L U Decomposition for Algebraic Positive Definite Systems. In: Hackbusch, W., Wittum, G. (eds) Incomplete Decomposition (ILU) — Algorithms, Theory, and Applications. Notes on Numerical Fluid Mechanics (NNFM), vol 29. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-322-85732-3_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-322-85732-3_13

  • Publisher Name: Vieweg+Teubner Verlag, Wiesbaden

  • Print ISBN: 978-3-528-07641-2

  • Online ISBN: 978-3-322-85732-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation