Istituto di Scienza e Tecnologie dell'Informazione     
Romani F. Complexity measures for matrix multiplication algorithms. In: Calcolo, vol. 17 pp. 77 - 86. 1980.
A new class of algorithms for the computation or 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 logarirhmic factor.

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