Skip to main content
SpringerLink
Log in

Fast Multiplication and Sparse Structures

  • Published:
Programming and Computer Software Aims and scope Submit manuscript

Abstract

The applicability of fast multiplication algorithms to sparse structures is discussed. Estimates for the degree of sparseness of matrices and polynomials are given for which fast multiplication algorithms have advantages over standard multiplication algorithms in terms of the multiplicative complexity. Specifically, the Karatsuba and Strassen algorithms are studied under the assumption of the uniform distribution of zero elements.

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. Karatsuba, A. and Ofman, Yu.P., Multiplication of Multivalued Numbers on Automata, Dokl. Akad. Nauk SSSR, 1962, vol. 145,no. 2, pp. 293–294.

    Google Scholar 

  2. Strassen, V., Gaussian Elimination Is Not Optimal, Numerische Mathematik, 1969, vol. 13, pp. 354–356.

    Google Scholar 

  3. Knuth, D.E., The Art of Computer Programming, vol. 2: Seminumerical Algorithms, Reading: Addison-Wesley, 1969. Translated under the title Iskusstvo programmirovaniya dlya EVM, tom 2: Poluchislennye algoritmy, Moscow: Mir, 1977.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Physics, and Informatics, Derzhavin State University, ul. Internatsional'naya 33, Tambov, 392622, Russia

    G. I. Malaschonok & E. S. Satina

Authors
  1. G. I. Malaschonok
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. S. Satina
    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

Malaschonok, G.I., Satina, E.S. Fast Multiplication and Sparse Structures. Programming and Computer Software 30, 105–109 (2004). https://doi.org/10.1023/B:PACS.0000021269.20049.0f

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:PACS.0000021269.20049.0f

Keywords

Search

Navigation