skip to main content
10.1145/800191.805516acmconferencesArticle/Chapter ViewAbstractPublication Pagesacm-national-conferenceConference Proceedingsconference-collections
Article
Free Access

A note on matrix multiplication in a paging environment

Published:20 October 1976Publication History

ABSTRACT

In order to minimize the number of page fetches required when multiplying matrices occupying many pages of virtual storage, we consider adapting Strassen-like recursive methods to a paging environment. An algorithm with a theoretically better rate of growth results. Also presented is an algorithm for efficiently converting matrices from row storage form to sub-matrix storage form, thus making more accessible the benefits of algorithms based on sub-matrix storage form which were presented in [5].

References

  1. 1.J. L. Elshoff, Some programming techniques for processing multi-dimensional matrices in a paging environment, Research Publication GMR-1483, General Motors Research Laboratories, Warren, Mich., October 1973.Google ScholarGoogle Scholar
  2. 2.P. C. Fischer, Further schemes for combining matrix algorithms, in Automata, Languages and Programming-2nd Colloquium, ed. J. Loeckx, Springer-Verlag, Berlin-Heidelberg, 1974, 428-436. Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. 3.P. C. Fischer and R. L. Probert, Efficient procedures for using matrix algorithms, ibid., 413-427. Google ScholarGoogle ScholarDigital LibraryDigital Library
  4. 4.R. W. Floyd, Permuting information in idealized two-level storage, in Complexity of Computer Computations, ed. R. E. Miller and J. W. Thatcher, Plenum Press, New York-London, 1972, 105-109.Google ScholarGoogle Scholar
  5. 5.A. C. McKellar and E. G. Coffman, Jr., Organizing matrices and matrix operations for paged memory systems, Communications of the ACM, Vol. 12, No. 3, March 1969, 153-165. Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. 6.C. B. Moler, Matrix computations with Fortran and paging, Communications of the ACM, Vol. 15, No. 4, April 1972, 268-270. Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. 7.R. L. Probert, On the additive complexity of matrix multiplication, SIAM J. on Computing, Vol. 5, No. 2, June 1976, 187-203.Google ScholarGoogle ScholarCross RefCross Ref
  8. 8.A. C. Shaw, The Logical Design of Operating Systems, Prentice-Hall, Englewood Cliffs, N. J., 1974. Google ScholarGoogle ScholarDigital LibraryDigital Library
  9. 9.V. Strassen, Gaussian elimination is not optimal, Numerische Mathematik, Vol. 13, 1969, 354-356.Google ScholarGoogle ScholarDigital LibraryDigital Library

Index Terms

  1. A note on matrix multiplication in a paging environment

          Recommendations

          Comments

          Login options

          Check if you have access through your login credentials or your institution to get full access on this article.

          Sign in
          • Published in

            cover image ACM Conferences
            ACM '76: Proceedings of the 1976 annual conference
            October 1976
            576 pages
            ISBN:9781450374897
            DOI:10.1145/800191

            Copyright © 1976 ACM

            Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

            Publisher

            Association for Computing Machinery

            New York, NY, United States

            Publication History

            • Published: 20 October 1976

            Permissions

            Request permissions about this article.

            Request Permissions

            Check for updates

            Qualifiers

            • Article

          PDF Format

          View or Download as a PDF file.

          PDF

          eReader

          View online with eReader.

          eReader