Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
SpringerLink
Log in

Relations between exact and approximate bilinear algorithms. Applications

  • Published:
CALCOLO Aims and scope Submit manuscript

Abstract

The relation betweenAPA-algorithms (i. e. approximating the result with an arbitrarily small error) andEC-algorithms (i. e. computing exactly the result) is analyzed. The existence of anAPA-algorithm of complexityt 0 and degreed implics the existence of anEC-algorithm of complexity (1+d)t 0. An application is given for problems associated to tensorial powers of a tensor, such as matrix product.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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. Bini D.,Border Rank of a p×q×2 Tensor and the Optimal Approximation of a Pair of Bilinear Forms. Lecture Notes on Computer Science85. Automata Languages and Programming (1980).

  2. Bini, D., Capovani M., Lotti G., Romani F., 0(n 2.7799)Complexity for n×n Approximate Matrix Multiplication. Information Processing Letters8 n0 5, (June 1979), 234–235.

    Article  MATH  MathSciNet  Google Scholar 

  3. Bini D., Lotti G., Romani F.,Approximate Solution for the Bilinear Form Computational Problem. SIAM J. Comp. (to appear).

  4. Egervary E.,On Hypermatrices whose Blocks are Commutable in Pairs and their Application in Lattice-Dynamics. Acta Sci. Math. (Szeged),15, (1954), 211–222.

    MATH  MathSciNet  Google Scholar 

  5. Isaacson E., Keller H. B.,Analysis of Numerical Methods. Jhon Wiley and Sons, New York 1966.

    MATH  Google Scholar 

  6. Pan V. Ya.,New Fast Algorithms for Matrix Operations. SIAM J. Comp.9 n0 2 (1980), 321–341.

    Article  MATH  Google Scholar 

  7. Pan V., Ya., Winograd S.,Personal Communication.

  8. Paterson M. S.,Complexity of Matrix Algorithms in Foundations of Computer Science. Mathematical Centre Tracts,63, Amsterdam (1975).

  9. Pease M. C.,Methods of Matrix Algebra, Academic Press New York, (1965).

    MATH  Google Scholar 

  10. Schonhage A.,Total and Partial Matrix Multiplication. Tech. Rep., Mathematisches Institute of Universitat. Tubingen, (1980).

    Google Scholar 

  11. Strassen V.,Gaussian Elimination is not Optimal. Numer. Math.13, (1969), 354–356.

    Article  MATH  MathSciNet  Google Scholar 

  12. Strassen V.,Vermeidung von Divisionen, J. Reine Angew. Math.246, (1975), 184–202.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Istituto di Matematica dell'Università di Pisa, Pisa, Italy

    D. Bini

Authors
  1. D. Bini
    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

Bini, D. Relations between exact and approximate bilinear algorithms. Applications. Calcolo 17, 87–97 (1980). https://doi.org/10.1007/BF02575865

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02575865

Keywords

Search

Navigation