Efficient procedures for using matrix algorithms

  • Patrick C. Fischer
  • Robert L. Probert
Thursday Afternoon
Part of the Lecture Notes in Computer Science book series (LNCS, volume 14)


A set of basic procedures for constructing matrix multiplication algorithms is defined. Five classes of composite matrix multiplication algorithms are considered and an optimal strategy is presented for each class. Instances are given of improvements in arithmetic cost over Strassen's method for multiplying square matrices. Best and worst case cost coefficients for matrix multiplication are given.

A similar analysis is done for matrix inversion algorithms.


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  1. Strassen, V., Gaussian elimination is not optimal, Numer.Math. 13 (1969), 354–356.Google Scholar
  2. Probert, R., On the complexity of matrix multiplication, Tech. Report CS-73-27 (1973), Dept. of Applied Analysis and Computer Science, University of Waterloo.Google Scholar
  3. Winograd, S., On multiplication of 2 × 2 matrices, Linear Algebra and its applications 4(1971), 381–388.CrossRefGoogle Scholar
  4. Fischer, P.C., Further schemes for combining matrix algorithms, Proc. 2nd Colloquium on Automata, Languages, and Programming (1974).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1974

Authors and Affiliations

  • Patrick C. Fischer
    • 1
  • Robert L. Probert
    • 2
  1. 1.University of WaterlooCanada
  2. 2.University of SaskatchewanCanada

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