Skip to main content
SpringerLink
Log in

On some parallel algorithms for inverting tridiagonal and pentadiagonal matrices

  • Published:
CALCOLO Aims and scope Submit manuscript

Abstract

We illustrate some 0 (logn) parallel algorithms for invertingn×n tridiagonal and pentadiagonal matrices. Also, an 0(logn) parallel algorithm is proposed to computer th order linear recurrences and the determinant ofr-band Hessenberg matrices.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. R. Bevilacqua, M. Capovani,Proprietà delle matrici tridiagonali ad elementi ed a blocchi, (1972), Ed. Tecnico Scientifica, Pisa.

    Google Scholar 

  2. R. Bevilacqua, M. Capovani,Proprietà delle matrici a banda ad elementi ed elementi ed a blocchi, Boll. U. M. I. 13-B (1976), 844–861.

  3. M. Capovani,Sulla determinazione della inversa delle matrici tridiagonali e tridiagonali a blocchi, Calcolo7 (1970), 295–303.

    Article  MathSciNet  Google Scholar 

  4. M. Capovani,Su alcune proprietà delle matrici tridiagonali e pentadiagonali, Calcolo8 (1971), 149–160.

    MATH  MathSciNet  Google Scholar 

  5. S. C. Chen, D. J. Kuck,Time and parallel processors bounds for linear recurrence systems, IEEE Trans. Computers, C-24 (1975), 701–717.

    MATH  MathSciNet  Google Scholar 

  6. L. Csanky,On parallel complexity of some computational problems, Dissertation University of California, Berkeley, (1974).

    Google Scholar 

  7. B. G. Greenberg, A. E. Sarhan,Matrix inversion, its interest and application in analysis of data, J. Amer. Statist., Assoc.,54 (1959), 755–766.

    Article  MATH  MathSciNet  Google Scholar 

  8. D. Heller,Some aspects of the cyclic reduction algorithm for block tridiagonal linear systems, ICASE, Hampton, Va., Dept. of Computer Science, Carnegie-Mellon University, December 1974.

    Google Scholar 

  9. D. Heller,A determinant theorem with application to parallel algorithms, SIAM J. Numer. Anal.,11 (1974), 559–568.

    Article  MATH  MathSciNet  Google Scholar 

  10. D. Heller,A Survey of parallel algorithms in numerical linear algebra, Dept. of Computer Science, Carnegie-Mellon University, February 1976.

  11. L. Hyafil, H. T. Kung,Bounds on the speedups of parallel evaluation of recurrences, Second USA-Japan Comp. Conf. Proc., August, 1975, 178–182.

  12. H. T. Kung,The structure of parallel algorithms, to appear in the forthcoming, Advances in Computers, Vol. 19, Academic Press.

  13. F. P. Preparata, J. Vullemin,The cube-connected cycles: a versatile network for parallel computation, University of Illinois, Urbana (1979).

    Google Scholar 

  14. F. P. Preparata, D. V. Sarwate,An improved parallel processors bound in fast matrix inversion, Information Processing Lett.,7 (1978), 148–150.

    Article  MATH  MathSciNet  Google Scholar 

  15. A. H. Sameh, D. J. Kuck,A parallel QR algorithm for symmetric tridiagonal matrices, IEEE Trans. Computers, C-26 (1977), 147–153.

    MATH  MathSciNet  Google Scholar 

  16. A. H. Sameh, D. J. Kuck,On stable parallel linear system solvers, J. Assoc. Comput. Mach.,25 (1978), 81–91.

    MATH  MathSciNet  Google Scholar 

  17. A. H. Sameh, S. C. Chen, D. J. Kuck,Parallel Poisson and Biharmonic solvers, Computing17 (1976), 219–230.

    Article  MATH  MathSciNet  Google Scholar 

  18. A. H. Sameh, R. P. Brent,Solving triangular linear systems of equations, SIAM J. Numer. Anal.,6 (1977).

  19. H. S. Stone,An efficient parallel algorithm for the solution of a tridiagonal linear system of equations, J. Assoc. Comput. Mach.,20 (1973), 27–38.

    MATH  MathSciNet  Google Scholar 

  20. P. N. Swarztrauber,A parallel algorithm for solving general tridiagonal equations, Math. Comput.,33 (1979), 185–199.

    Article  MATH  MathSciNet  Google Scholar 

  21. C. D. Thompson,A complexity Theory for VLSI, Dept. of Computer Science, Carnegie-Mellon University, July 1979.

Download references

Author information

Authors and Affiliations

  1. Istituto di Scienze dell'Informazione, Corso Italia 40, 56100, Pisa, Italy

    P. Zellini

Authors
  1. S. Cei
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Galli
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Soccio
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. P. Zellini
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cei, S., Galli, M., Soccio, M. et al. On some parallel algorithms for inverting tridiagonal and pentadiagonal matrices. Calcolo 18, 303–319 (1981). https://doi.org/10.1007/BF02576433

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02576433

Keywords

Search

Navigation