Correction of 'J. Laderman, V. Pan, X. H. Sha, On practical Algorithms for Accelerated Matrix Multiplication, Linear Algebra and its Applications. Vol. 162-164 (1992) pp. 557-5

02/15/2023

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by   Jerzy S. Respondek, et al.

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In this article we corrected the trilinear formula for triple disjoint matrix multiplication given in the article 'J. Laderman, V. Pan, X. H. Sha, On practical Algorithms for Accelerated Matrix Multiplication, Linear Algebra and its Applications. Vol. 162-164 (1992) pp. 557-588', which is incorrect for matrix dimensions equal to two or greater. That formula is a base of two algorithms, for disjoint and single matrix multiplication. The necessary correction made the amount of non scalar products raise, slightly increasing the algorithm time complexity. We also corrected explicit formulas, in the bilinear form, for triple disjoint matrix multiplication. They are explicit, thus convenient for practical use of fast matrix multiplication algorithms in question.