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. 557-588'

• Published in: Linear & multilinear algebra Vol. 73; no. 5; pp. 838 - 848
• Main Author: Respondek, Jerzy S.
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 24.03.2025; Taylor & Francis Ltd
• Subjects: Algorithms; Fast matrix multiplication; Linear algebra; Matrices (mathematics); matrix algebra; Multiplication; numerical mathematics
• ISSN: 0308-1087; 1563-5139
• DOI: 10.1080/03081087.2024.2391807

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 rise, slightly increasing the algorithm time complexity. We also corrected explicit formulas, in the bilinear form, for triple disjoint matrix multiplication. They are explicit, and thus convenient for the practical use of the fast matrix multiplication algorithms in question.