Development of high speed singular value decomposition algorithm for sparse matrices of large scale and upload of its source code

2015 Fiscal Year Final Research Report

• Project/Area Number: 24360038
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Partial Multi-year Fund
• Section: 一般
• Research Field: Engineering fundamentals
• Research Institution: Kyoto University
• Principal Investigator: Nakamura Yoshimasa 京都大学, 情報学研究科, 教授 (50172458)
• Co-Investigator(Kenkyū-buntansha): KIMURA Kinji 京都大学, 大学院情報学研究科, 特定准教授 (10447899)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Keywords: 特異値分解 / 大規模スパース行列 / Golub-Kahan-Lanczos法 / 部分特異対 / 再直交化

Outline of Final Research Achievements

Singular value decomposition of sparse matrices of large scale is an important matrix operation which is fundamental for analyzing big data. In this research we apply the Golub-Kahan-Lanczos algorithm with reorthogonalization to sparse matrices of large scale to generate approximated tridiagonal matrices by high performance computation in parallel processing. Secondly the bisection and the inverse iteration methods are applied to them to giving a subset of eigenpairs of the originals with high reusability of data. The corresponding source codes have been uploaded one by one. When the sparse matrices are positive definite, then the resulting eigenpairs lead to a sebset of singular triplets.

Free Research Field

計算数学