Istituto di Scienza e Tecnologie dell'Informazione     
Bini D., Capovani M. Su alcune questioni di complessita' computazionale numerica. In: Bollettino Della Unione Matematica Italiana, vol. 15 A pp. 327 - 351. Zanichelli, 1978.
In this paper we make an attempt to introduce some aspects of the field of numerical computational complexity. We use the matrix multiplication problem to illustrate general features of algebraic complexity: at the heart of a number of problem in minimizing the number of multiplications required to perform a calculation there is a problem in matrix algebra relating to the expansions of a given set of matrices as linear combinations of rank one matrices. Here an approach on this problem is presented, with some general results and easily applicable criterions for evaluating lower bounds on the number of multiplications.

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