On wiedemann's method of solving sparse linear systems

  • Erich Kaltofen
  • B. David Saunders
Invited Contributions
Part of the Lecture Notes in Computer Science book series (LNCS, volume 539)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature Cited

  1. Abdali, S. K. and Wise, D. S., “Experiments with quadtree representation of matrices,” Proc. ISSAC '88, Springer Lect. Notes Comput. Sci. 358, pp. 467–474 (1988).Google Scholar
  2. Beneš, V. E., “Optimal rearrangeable multistage connecting networks,” Bell System Tech. J. 43, pp. 1641–1656 (1964)Google Scholar
  3. Canny, J., Kaltofen, E., and Lakshman, Yagati, “Solving systems of non-linear polynomial equations faster,” Proc. ACM-SIGSAM 1989 Internat. Symp. Symbolic Algebraic Comput., pp. 121–128 (1989).Google Scholar
  4. Cantor, D. G. and Kaltofen, E., “Fast multiplication of polynomials over arbitrary rings,” Tech. Report 87-35, Dept. Comput. Sci., Rensselaer Polytechnic Institute, December 1987. Revised version to appear in Acta Informatica.Google Scholar
  5. Golub, G. H. and van Loan, C. F., Matrix Computations; Johns Hopkins University Press, Baltimore, Maryland, 1987.Google Scholar
  6. Hardy, G. H. and Wright, E. M., An Introduction to the Theory of Numbers; Oxford Univ. Press, Oxford, 1979.Google Scholar
  7. Kaltofen, E. and Pan, V., “Processor efficient parallel solution of linear systems over an abstract field,” in Proc. 3rd Ann. ACM Symp. Parallel Algor. Architecture; ACM Press, p. to appear, 1991.Google Scholar
  8. Kaltofen, E. and Rolletschek, H., “Computing greatest common divisors and factorizations in quadratic number fields,” Math. Comp. 53/188, pp. 697–720 (1989).Google Scholar
  9. Kaminski, M., Kirkpatrick, D. G., and Bshouty, N. H., “Addition requirements for matrix and transposed matrix products,” J. Algorithms 9, pp. 354–364 (1988).Google Scholar
  10. LaMacchia, B. A. and Odlyzko, A. M., “Solving large sparse linear systems over finite fields,” in Advances in Cryptology: Crypto 90, Lect. Notes Comput. Sci., edited by S. Vanstone; Springer Verlag, p. to appear, 1991.Google Scholar
  11. Lipton, R., Rose, D., and Tarjan, R. E., “Generalized nested dissection,” SIAM J. Numer. Anal. 16, pp. 346–358 (1979).Google Scholar
  12. Massey, J. L., “Shift-register synthesis and BCH decoding,” IEEE Trans. Inf. Theory IT-15, pp. 122–127 (1969).Google Scholar
  13. Schwartz, J. T., “Fast probabilistic algorithms for verification of polynomial identities,” J. ACM 27, pp. 701–717 (1980).Google Scholar
  14. Wiedemann, D., “Solving sparse linear equations over finite fields,” IEEE Trans. Inf. Theory IT-32, pp. 54–62 (1986).Google Scholar
  15. Wise, D. S. and Franco, J., “Costs of quadtree representation of non-dense matrices,” J. Parallel Distributed Comput. 9, pp. 282–296 (1990).Google Scholar
  16. Zippel, R. E., “Probabilistic algorithms for sparse polynomials,” Proc. EUROSAM '79, Springer Lec. Notes Comp. Sci. 72, pp. 216–226 (1979).Google Scholar

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Erich Kaltofen
    • 1
  • B. David Saunders
    • 2
  1. 1.Department of Computer ScienceRensselaer Polytechnic InstituteTroy
  2. 2.Department of Computer and Information SciencesUniversity of DelawareNewark

Personalised recommendations