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Complexity measures for matrix multiplication algorithms

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Abstract

A new class of algorithms for the computation of bilinear forms has been recently introduced [1, 3]. These algorithms approximate the result with an arbitrarily small error. Such approximate algorithms may have a multiplicative complexity smaller than exact ones. On the other hand any comparison between approximate and exact algorithms has to take into account the complexity-stability relations.

In this paper some complexity measures for matrix multiplication algorithms are discussed and applied to the evaluation of exact and approximate algorithms. Multiplicative complexity is shown to remain a valid comparison test and the cost of approximation appears to be only a logarithmic factor.

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References

  1. D. Bini, M. Capovani, G. Lotti, F. Romani,O (n 2.7799),Complexity for n×n Matrix Multiplication. IEI Report B 78-27, (1978).

  2. D. Bini, G. Lotti, F. Romani,Stability and Complexity in the Evaluation of a Set of Bilinear Forms. IEI Report B 78-25, (1978).

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Authors and Affiliations

  1. Istituto di Elaborazione della Informazione, CNR, Pisa

    F. Romani

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  1. F. Romani
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Romani, F. Complexity measures for matrix multiplication algorithms. Calcolo 17, 77–86 (1980). https://doi.org/10.1007/BF02575864

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  • DOI: https://doi.org/10.1007/BF02575864

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