Skip to main content

A Homotopic Residual Correction Process

  • Conference paper
  • First Online:
Book cover Numerical Analysis and Its Applications (NAA 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1988))

Included in the following conference series:

Abstract

We present a homotopic residual correction algorithm for the computation of the inverses and generalized inverses of structured matrices. The algorithm simplifies the process proposed in [P92], and so does our analysis of its convergence rate, compared to [P92]. The algorithm promises to be practically useful.

Supported by NSF Grant CCR9732206 and PSC CUNY Award 61393-0030.

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 109.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 139.99
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. D. A. Bini, B. Meini, Approximate Displacement Rank and Applications, preprint.

    Google Scholar 

  2. E. Issacson, H. B. Keller, Analysis of Numerical Methods, Wiley, New York, 1966.

    Google Scholar 

  3. V. Y. Pan, Parallel Solution of Toeplitz-like Linear Systems, J. of Complexity, 8, 1–21, 1992.

    Article  Google Scholar 

  4. V. Y. Pan, Decreasing the Displacement Rank of a Matrix, SIAM J. Matrix Anal. Appl., 14, 1, 118–121, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  5. V. Y. Pan, Concurrent Iterative Algorithm for Toepliz-like Linear Systems, IEEE Trans. on Parallel and Distributed Systems, 4, 5, 592–600, 1993.

    Article  Google Scholar 

  6. V. Y. Pan, Superfast Computations with Structured Matrices: Unified Study, preprint, 2000.

    Google Scholar 

  7. B. N. Parlett, The Symmetric Eigenvalue Problem, Prentice-Hall, Englewood Cliffs, NJ, 1980.

    MATH  Google Scholar 

  8. V. Y. Pan, S. Branham, R. Rosholt, A. Zheng, Newton’s Iteration for Structured Matrices and Linear Systems of Equations, SIAM volume on Fast Reliable Algorithms for Matrices with Structure, SIAM Publications, Philadelphia, 1999.

    Google Scholar 

  9. V. Y. Pan, Y. Rami, Newton’s iteration for the Inversion of Structured Matrices, Structured Matrices: Recent Developments in Theory and Computation, edited by D. Bini, E. Tyrtyshnikov and P. Yalamov, Nova Science Publishers, USA, 2000.

    Google Scholar 

  10. V. Y. Pan, Y. Rami, X. Wang, Newton’s iteration for the Inversion of Structured Matrices, Proc.14th Intern. Symposium on Math. Theory of Network and Systems (MTNS’2000), June 2000.

    Google Scholar 

  11. V. Y. Pan, Y. Rami, X. Wang, Structured Matrices and Newton’s Iteration: Unified Approach, preprint.

    Google Scholar 

  12. V. Y. Pan, R. Schreiber, An Improved Newton Iteration for the Generalized Inverse of a Matrix, with Applications, SIAM J. on Scientific and Statistical Computing, 12, 5, 1109–1131, 1991.

    Article  MATH  MathSciNet  Google Scholar 

  13. V. Y. Pan, A. Zheng, X. Huang, O. Dias, Newton’s Iteration for Inversion of Cauchy-like and Other Structured Matrices, J. of Complexity, 13, 108–124, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  14. G. Schultz, Iterative Berechnung der Reciproken Matrix, Z. Angew. Meth. Mech., 13, 57–59, 1933.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Pan, V.Y. (2001). A Homotopic Residual Correction Process. In: Vulkov, L., Yalamov, P., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2000. Lecture Notes in Computer Science, vol 1988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45262-1_76

Download citation

  • DOI: https://doi.org/10.1007/3-540-45262-1_76

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41814-6

  • Online ISBN: 978-3-540-45262-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics