提高快速矩阵乘法的稳定性

IF 1.7 3区数学 Q2 MATHEMATICS, APPLIED

Numerical Algorithms Pub Date : 2024-04-20 DOI:10.1007/s11075-024-01806-y

Charlotte Vermeylen, Marc Van Barel

引用次数: 0

摘要

我们采用增量拉格朗日方法，最小化受限最小二乘成本函数，旨在找到具有矩阵乘法张量最大值有界元素的稀疏多面体分解。我们利用这种方法获得了新的分解和分解的参数族。利用这些参数化，我们发现了更快、更稳定的矩阵乘法算法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Stability improvements for fast matrix multiplication

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Stability improvements for fast matrix multiplication

We implement an Augmented Lagrangian method to minimize a constrained least-squares cost function designed to find sparse polyadic decompositions with elements of bounded maximal value of matrix multiplication tensors. We use this method to obtain new decompositions and parameter families of decompositions. Using these parametrizations, faster and more stable matrix multiplication algorithms are discovered.

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来源期刊

Numerical Algorithms 数学-应用数学

CiteScore

4.00

自引率

9.50%

发文量

201

审稿时长

9 months

期刊介绍： The journal Numerical Algorithms is devoted to numerical algorithms. It publishes original and review papers on all the aspects of numerical algorithms: new algorithms, theoretical results, implementation, numerical stability, complexity, parallel computing, subroutines, and applications. Papers on computer algebra related to obtaining numerical results will also be considered. It is intended to publish only high quality papers containing material not published elsewhere.