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Development of robust and efficient algorithms in numerical linear algebra

Research Project

Project/Area Number 23700023
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Fundamental theory of informatics
Research InstitutionTokyo Woman's Christian University

Principal Investigator

OGITA Takeshi  東京女子大学, 現代教養学部, 准教授 (00339615)

Project Period (FY) 2011-04-28 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Keywords数値線形代数 / 行列分解 / 高精度計算 / 悪条件問題 / 数値計算手法 / アルゴリズム / 行列解析 / 情報基礎 / 数値計算
Outline of Final Research Achievements

The purpose of this research is to create a framework of robust matrix factorization algorithms in numerical linear algebra. Since scientific computing is based on numerical linear algebra, development of such algorithms is very important. For this purpose, it was necessary to create a common framework for algorithms rather than considering details of individual algorithms. We succeeded in developing a robust factorization algorithm for real symmetric matrices. Moreover, we proposed robust numerical methods for eigenvalue problems and singular value problems.

Report

(5 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Research-status Report
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (31 results)

All 2015 2014 2013 2012 2011 Other

All Journal Article (9 results) (of which Peer Reviewed: 9 results,  Open Access: 1 results) Presentation (19 results) (of which Invited: 6 results) Book (1 results) Remarks (2 results)

  • [Journal Article] A fast and efficient algorithm for solving ill-conditioned linear systems2015

    • Author(s)
      Y. Kobayashi, T. Ogita
    • Journal Title

      JSIAM Letters

      Volume: 7 Issue: 0 Pages: 1-4

    • DOI

      10.14495/jsiaml.7.1

    • NAID

      130004953464

    • ISSN
      1883-0609, 1883-0617
    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Fast verified solutions of sparse linear systems with H-matrices2013

    • Author(s)
      A. Minamihata, K. Sekine, T. Ogita, S. Oishi
    • Journal Title

      Reliable Computing

      Volume: 19 Pages: 127-141

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Convergence analysis of accurate inverse Cholesky factorization2013

    • Author(s)
      Y. Yanagisawa, T. Ogita
    • Journal Title

      JSIAM Letters

      Volume: 5 Pages: 25-28

    • NAID

      130003371116

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Generalization of error-free transformation for matrix multiplication and its application2013

    • Author(s)
      K. Ozaki, T. Ogita, S. Oishi, S. M. Rump
    • Journal Title

      Nonlinear Theory and Its Applications, IEICE

      Volume: 4 Issue: 1 Pages: 2-11

    • DOI

      10.1587/nolta.4.2

    • NAID

      130003375409

    • ISSN
      2185-4106
    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Robust computation of determinant2012

    • Author(s)
      T. Ogita
    • Journal Title

      AIP Conference Proceedings

      Volume: 1504 Pages: 1119-1123

    • DOI

      10.1063/1.4772123

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Matrix multiplication with guaranteed accuracy by level 3 BLAS2012

    • Author(s)
      K. Ozaki, T. Ogita, S. Oishi
    • Journal Title

      AIP Conference Proceedings

      Volume: 1504 Pages: 1128-1133

    • DOI

      10.1063/1.4772125

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Error-Free Transformation of Matrix Multiplication by Using Fast Routines of Matrix Multiplication and its Applications2012

    • Author(s)
      K. Ozaki, T. Ogita, S. Oishi, S. M. Rump
    • Journal Title

      Numerical Algorithms

      Volume: 59 Issue: 1 Pages: 95-118

    • DOI

      10.1007/s11075-011-9478-1

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Accurate and Verified Numerical Computation of the Matrix Determinant2012

    • Author(s)
      T. Ogita
    • Journal Title

      International Journal of Reliability and Safety

      Volume: 6 Issue: 1/2/3 Pages: 242-254

    • DOI

      10.1504/ijrs.2012.044287

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Accurate and robust inverse Cholesky factorization2012

    • Author(s)
      T. Ogita, S. Oishi
    • Journal Title

      Nonlinear Theory and Its Applications, IEICE

      Volume: 3 Issue: 1 Pages: 103-111

    • DOI

      10.1587/nolta.3.103

    • NAID

      130002139440

    • ISSN
      2185-4106
    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Presentation] Iterative Refinement for Symmetric Eigenvalue Decomposition2015

    • Author(s)
      T. Ogita
    • Organizer
      The First French-Japanese Workshop on Numerical Computations
    • Place of Presentation
      パリ(フランス)
    • Year and Date
      2015-03-25
    • Related Report
      2014 Annual Research Report
  • [Presentation] 対称固有値問題に対する残差反復法2014

    • Author(s)
      荻田 武史
    • Organizer
      RIMS研究集会「新時代の科学技術を牽引する数値解析学」
    • Place of Presentation
      京都大学数理解析研究所(京都府・京都市)
    • Year and Date
      2014-10-09
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Iterative Refinement for Symmetric Eigenvalue Problems2014

    • Author(s)
      T. Ogita
    • Organizer
      16th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics
    • Place of Presentation
      ヴュルツブルク(ドイツ)
    • Year and Date
      2014-09-22
    • Related Report
      2014 Annual Research Report
  • [Presentation] Acceleration of Accurate Floating-Point Summation2014

    • Author(s)
      T. Ogita
    • Organizer
      The Fifth China-Japan-Korea Conference on Numerical Mathematics
    • Place of Presentation
      銀川(中国)
    • Year and Date
      2014-08-27
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Iterative Refinement for Singular Value Decompositions2014

    • Author(s)
      T. Ogita
    • Organizer
      The 7th Small Workshop on Interval Methods (SWIM2014)
    • Place of Presentation
      ウプサラ(スウェーデン)
    • Year and Date
      2014-06-11
    • Related Report
      2014 Annual Research Report
  • [Presentation] Verified Solutions of Sparse Linear Systems2012

    • Author(s)
      T. Ogita
    • Organizer
      Fifth Conference on Numerical Analysis and Applications
    • Place of Presentation
      Lozenetz, Bulgaria,
    • Related Report
      2012 Research-status Report
  • [Presentation] Verified Solutions of Sparse Linear Systems2012

    • Author(s)
      T. Ogita
    • Organizer
      2012 SIAM Conference on Applied Linear Algebra
    • Place of Presentation
      Valencia, Spain
    • Related Report
      2012 Research-status Report
  • [Presentation] Verified Solutions of Sparse Linear Systems2012

    • Author(s)
      T. Ogita
    • Organizer
      The 15th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic and Verified Numerical Computations
    • Place of Presentation
      Novosibirsk, Russia
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Backward Error Bounds of Block LDLT Factorizations2012

    • Author(s)
      T. Ogita
    • Organizer
      2012 International Symposium on Nonlinear Theory and its Applications
    • Place of Presentation
      Palma de Mallorca, Spain
    • Related Report
      2012 Research-status Report
  • [Presentation] 連立一次方程式に対する精度保証の現状2012

    • Author(s)
      荻田 武史
    • Organizer
      第4回横幹連合総合シンポジウム
    • Place of Presentation
      日本大学 生産工学部 津田沼キャンパス
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] 線形問題に対する精度保証付き数値計算2012

    • Author(s)
      荻田 武史
    • Organizer
      第2回計算力学シンポジウム
    • Place of Presentation
      日本学術会議講堂
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Robust Inverse Matrix Factorizations2011

    • Author(s)
      T. Ogita
    • Organizer
      International Workshop on Numerical Linear Algebra and Its Applications
    • Place of Presentation
      Tongji University, Shanghai, China
    • Related Report
      2011 Research-status Report
  • [Presentation] Computing Tight Bounds on Extreme Eigenvalues of Symmetric Matrices2011

    • Author(s)
      T. Ogita
    • Organizer
      2011 International Symposium on Nonlinear Theory and its Applications
    • Place of Presentation
      Kobe, Japan
    • Related Report
      2011 Research-status Report
  • [Presentation] Rigorous backward error bounds on factorizations of symmetric indefinite matrices

    • Author(s)
      T. Ogita, K. Kobayashi
    • Organizer
      4th International Conference on Matrix Analysis and Applications
    • Place of Presentation
      Konya, Turkey
    • Related Report
      2013 Research-status Report
  • [Presentation] Backward error bounds on factorizations of symmetric indefinite matrices

    • Author(s)
      T. Ogita
    • Organizer
      The 10th European Conference on Numerical Mathematics and Advanced Applications
    • Place of Presentation
      Lausanne, Switzerland
    • Related Report
      2013 Research-status Report
  • [Presentation] Verified Solutions of Sparse Linear Systems with Special Matrices

    • Author(s)
      T. Ogita
    • Organizer
      2013 International Symposium on Nonlinear Theory and its Applications
    • Place of Presentation
      Santa Fe, USA
    • Related Report
      2013 Research-status Report
  • [Presentation] 精度保証付き数値計算と高精度計算

    • Author(s)
      荻田 武史
    • Organizer
      2013年度 応用数学合同研究集会
    • Place of Presentation
      龍谷大学 瀬田キャンパス
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Fast verified solutions of sparse linear systems

    • Author(s)
      T. Ogita
    • Organizer
      The International Workshop on Numerical Verification and its Applications 2014
    • Place of Presentation
      Waseda University, Tokyo
    • Related Report
      2013 Research-status Report
  • [Presentation] Iterative Refinement for Symmetric Eigenvalue Problems

    • Author(s)
      T. Ogita
    • Organizer
      日本応用数理学会 研究部会連合発表会
    • Place of Presentation
      京都大学
    • Related Report
      2013 Research-status Report
  • [Book] 応用数理ハンドブック2013

    • Author(s)
      日本応用数理学会 監修/薩摩順吉 ・大石進一 ・杉原正顕 編
    • Total Pages
      8
    • Publisher
      朝倉書店
    • Related Report
      2013 Research-status Report
  • [Remarks] 荻田 武史 - 東京女子大学

    • URL

      http://www.twcu.ac.jp/dept_grad/teacherlist/takeshi-ogita.html

    • Related Report
      2012 Research-status Report
  • [Remarks]

    • URL

      http://www.math.twcu.ac.jp/~ogita/math/math.htm

    • Related Report
      2011 Research-status Report

URL: 

Published: 2011-08-05   Modified: 2019-07-29  

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