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

Research Project

Project/Area Number 24560518
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Measurement engineering
Research InstitutionUniversity 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
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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 / 悪条件問題 / 最小自乗問題 / グラム・シュミット法 / 大規模問題 / 反復解法 / 正則化法 / 逆問題
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.

Report

(4 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Research-status Report
  • 2012 Research-status Report
  • Research Products

    (2 results)

All 2015 2014

All Journal Article (1 results) (of which Peer Reviewed: 1 results,  Acknowledgement Compliant: 1 results) Presentation (1 results)

  • [Journal Article] A new QR factorization method by recursive blocked Gram-Schmidt algorithm and recursive blocked Cholesky factorization2015

    • Author(s)
      Shinya Ozawa, Yohsuke Hosoda and Takemitsu Hasegawa
    • Journal Title

      AIP Conference Proceedings

      Volume: 1648 Pages: 1-4

    • DOI

      10.1063/1.4912918

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Presentation] A new QR factorization method by recursive blocked Gram-Schmidt algorithm and recursive blocked Cholesky factorization2014

    • Author(s)
      Shinya Ozawa, Yohsuke Hosoda and Takemitsu Hasegawa
    • Organizer
      12th International Conference of Numerical Analysis and Applied Mathematics
    • Place of Presentation
      Rhodes, Greece
    • Year and Date
      2014-09-22 – 2014-09-28
    • Related Report
      2014 Annual Research Report

URL: 

Published: 2013-05-31   Modified: 2019-07-29  

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