Development of numerical methods for solving large-scale ill-conditioned linear system of equations and its applications

2014 Fiscal Year Final Research Report

• Project/Area Number: 24560518
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Measurement engineering
• Research Institution: University of Fukui
• Principal Investigator: HOSODA Yohsuke 福井大学, 工学(系)研究科(研究院), 教授 (80264951)
• Co-Investigator(Kenkyū-buntansha): HASEGAWA Takemitsu 福井大学, 大学院工学研究科, 名誉教授 (70023314)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 悪条件線形方程式 / 特異値分解 / QR分解 / ブロック化アルゴリズム

Outline of Final Research Achievements

The purpose of our study is to develop new numerical methods for solving large-scale ill-conditioned linear system of equations. For dense matrices, numerical methods based on the singular value decomposition (SVD) have been used. However, these methods need high computational costs. To overcome such difficulties, we make use of numerical methods based on the QR decomposition instead of the SVD. We propose a new algorithm for efficiently computing the QR factorization of a given matrix. Our method uses a recursive blocked Gram-Schmidt orthogonalization and a recursive blocked Cholesky factorization. Numerical experiments show that our method is better than the conventional methods.

Free Research Field

数値解析