{"title":"Stability improvements for fast matrix multiplication","authors":"Charlotte Vermeylen, Marc Van Barel","doi":"10.1007/s11075-024-01806-y","DOIUrl":null,"url":null,"abstract":"<p>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.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":"87 1","pages":""},"PeriodicalIF":1.7000,"publicationDate":"2024-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Numerical Algorithms","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11075-024-01806-y","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
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.
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.
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