《J. Laderman, V. Pan, X. H. Sha,关于加速矩阵乘法的实际算法、线性代数及其应用的更正》,第162-164卷(1992年),第557-588页。 (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')

2023 年 2 月 15 日

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'

翻译：《J. Laderman, V. Pan, X. H. Sha,关于加速矩阵乘法的实际算法、线性代数及其应用的更正》,第162-164卷(1992年),第557-588页。

Jerzy S. Respondek

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.

翻译：在本条中,我们纠正了“J.Lademan, V.Pan, X.H. Sha,关于加速矩阵乘法的实际算法、线性代数及其应用”第162-164卷(1992年),第557-588页”这一三线公式,该公式对相当于两个或两个以上的矩阵维度是不正确的。该公式是两种算法的基础,一种是脱节和单一矩阵乘法。必要的修正使非标值产品数量增加,略微增加了算法时间复杂性。我们还修改了双线格式的明确公式,用于三线交错矩阵乘法。这些公式很明确,因此便于实际使用有关的快速矩阵乘法。