Fast numerical algorithms for singular value decompositions

2017 Fiscal Year Final Research Report

• Project/Area Number: 25790096
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Computational science
• Research Institution: The University of Tokyo
• Principal Investigator: AISHIMA Kensuke 東京大学, 大学院情報理工学系研究科, 特任講師 (40609658)
• Project Period (FY): 2013-04-01 – 2018-03-31
• Keywords: 数値線形代数

Outline of Final Research Achievements

In the modern information society, it is very important to develop fast algorithms for computing singular value decompositions of matrices because such numerical algorithms are fundamental in data science, artificial intelligence and so forth. In this study, we have provided convergence theory for singular value algorithms, which can be successfully applied to improvement of existing efficient algorithms. In addition, we have established similar important convergence theorems for eigenvalue algorithms. Moreover, using similar mathematical analysis, we have newly constructed convergence theorems for numerical algorithms for modern matrix computations successfully applied to information sciences. On the basis of the above convergence theorems, we have developed high performance algorithms for directly solving important problems in information sciences.

Free Research Field

数値解析，高性能計算，データサイエンス