Correction of ‘ <i>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</i> ’

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.

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Journal
Linear and Multilinear Algebra
Published
2024-08-19
DOI
https://doi.org/10.1080/03081087.2024.2391807
Primary Topic
Parallel Computing and Optimization Techniques
Type
article
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article

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 ’

Jerzy S. Respondek
Linear and Multilinear Algebra
Parallel Computing and Optimization Techniques
article

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 ’

Jerzy S. Respondek
article en

Abstract

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.

Linear and Multilinear AlgebraVol. 73(5)
Silesian University of Technology (PL)
Openalex Percentile: Top 87%
Parallel Computing and Optimization Techniques
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Correction of ‘ <i>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</i> ’ — Jerzy S. Respondek · Linear and Multilinear Algebra (2024) | TGRS Research Map | TGRS