Abstract
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.
This research was partially supported by National Research Council grants A5549 and A 8982.
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References
Strassen, V., Gaussian elimination is not optimal, Numer. Math. 13 (1969), 354–356.
Probert, R., On the complexity of matrix multiplication, Tech. Report CS-73–27 (1973), Dept. of Applied Analysis and Computer Science, University of Waterloo.
Winograd, S., On multiplication of 2 x 2 matrices, Linear Algebra and its applications 4 (1971), 381–388.
Fischer, P.C., Further schemes for combining matrix algorithms, Proc. 2nd Colloquium on Automata, Languages, and Programming (1974).
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Fischer, P.C., Probert, R.L. (1974). Efficient Procedures for Using Matrix Algorithms. In: Loeckx, J. (eds) Automata, Languages and Programming. ICALP 1974. Lecture Notes in Computer Science, vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21545-6_31
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DOI: https://doi.org/10.1007/978-3-662-21545-6_31
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-06841-9
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