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Study on fast and stable iterative methods for solving large and sparse linear systems arising from computational science

Research Project

Project/Area Number 18760063
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Engineering fundamentals
Research InstitutionNagoya University

Principal Investigator

SOGABE Tomohiro  Nagoya University, 大学院・工学研究科, 助教 (30420368)

Project Period (FY) 2006 – 2008
Project Status Completed (Fiscal Year 2008)
Budget Amount *help
¥3,870,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥270,000)
Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2007: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2006: ¥2,000,000 (Direct Cost: ¥2,000,000)
Keywords連立一次方程式 / クリロフ部分空間法 / 双共役残差法(Bi-CR法) / 積型解法 / CRS法 / 大規模連立一次方程式 / 双共役残差法 / 数値解析
Research Abstract

物理・工学に現れる超大規模連立一次方程式の高速・高安定解法を開発することを目的とし,近年提案されたBi-CR法を基礎として,計画通りその積型解法族が開発された.これらの解法族は,新規購入した計算機を用いて大規模な計算を行い,従来法であるBi-CG法の積型解法族と比べて,同程度以上の高速性と安定性を有することを確認した.その他,本研究と関連する前処理技術の開発,特殊行列の性質に関する基礎研究,そして複数の連立一次方程式を同時に解く高速解法の開発を行った.

Report

(4 results)
  • 2008 Annual Research Report   Final Research Report ( PDF )
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • Research Products

    (37 results)

All 2009 2008 2007 2006 Other

All Journal Article (24 results) (of which Peer Reviewed: 20 results) Presentation (12 results) Remarks (1 results)

  • [Journal Article] An extension of the conjugate residual method to nonsymmetric linear systems2009

    • Author(s)
      T. Sogabe, M. Sugihara, S. -L. Zhang
    • Journal Title

      Journal of Computational and Applied Mathematics 226

      Pages: 103-113

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] An extension of the conjugate residual method to nonsymmetric linear systems2009

    • Author(s)
      T.Sogabe, M.Sugihara, S.-L.Zhang
    • Journal Title

      J.Comput.Appl.Math. 226

      Pages: 103-113

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On a weighted quasi- residual minimization strategy for solving complex symmetric shifted linear systems2008

    • Author(s)
      T. Sogabe, T. Hoshi, S. -L. Zhang, T. Fujiwara
    • Journal Title

      Electronic Transac- tions on Numerical Analysis 31

      Pages: 126-140

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Journal of Physical Society of Japan2008

    • Author(s)
      S. Yamamoto, T. Sogabe, T. Hoshi, S. -L. Zhang, T. Fujiwara
    • Journal Title

      77 77,114713

      Pages: 1-8

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] New algorithms for solving periodic tridiagonal and periodic pentadiagonal linear systems2008

    • Author(s)
      T. Sogabe
    • Journal Title

      Appl ied Mathematics and Computation 202

      Pages: 850-856

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] A note on "A fast numerical algorithm for the determinant of a pentadiagonal matrix2008

    • Author(s)
      T. Sogabe
    • Journal Title

      Applied Mathe matics and Computation 201

      Pages: 561-564

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Numerical algorithms for solving comrade linear systems based on tridiagonal solvers2008

    • Author(s)
      T. Sogabe
    • Journal Title

      Applied Math ematics and Computation 198

      Pages: 117-122

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] A fast numerical algorithm for the determinant of a pentadiagonal matrix2008

    • Author(s)
      T. Sogabe
    • Journal Title

      Applied Mathematics and Com putation 196

      Pages: 835-841

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] AOR法を用いた可変的前処理付き一般化共役残差法2008

    • Author(s)
      前田祥兵, 曽我部知広, 他
    • Journal Title

      日本応用数理学会論文誌 18

      Pages: 155-170

    • Related Report
      2008 Final Research Report 2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On a weighted quasi-residual minimization strategy for solving complex symmetric shifted linear systems2008

    • Author(s)
      T.Sogabe, T.Hoshi, S.-L.Zhang, T.Fujiwara
    • Journal Title

      Electron.Trans.Numer.Anal. 31

      Pages: 126-140

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Shifted COCG method and its application to double orbital extended Hubbard model2008

    • Author(s)
      S.Yamamoto, T.Sogabe, T.Hoshi, S.-L.Zhang, T.Fujiwara
    • Journal Title

      J.Phys.Soc.Jpn. 77

      Pages: 1-8

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] New algorithms for solving periodic tridiagonal and periodic pentadiagonal linear systems2008

    • Author(s)
      T.Sogabe
    • Journal Title

      Appl.Math.Comput. 202

      Pages: 850-856

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A note on "A fast numerical algorithm for the determinant of a pentadiagonal matrix"2008

    • Author(s)
      T.Sogabe
    • Journal Title

      Appl.Math.Comput. 201

      Pages: 561-564

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Numerical algorithms for solving comrade linear systems based on tridiagonal solvers2008

    • Author(s)
      T.Sogabe
    • Journal Title

      Appl.Math.Comput. 198

      Pages: 117-122

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A fast numerical algorithm for the determinant of a pentadiagonal matrix2008

    • Author(s)
      T. Sogabe
    • Journal Title

      Applied Mathematics and Computation 196

      Pages: 835-841

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On a two-term recurrence for the determinant of a general matrix2007

    • Author(s)
      T. Sogabe
    • Journal Title

      Applied Mathematics and Com putation 187

      Pages: 785-788

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Finger patternのブロック化による陰的wavelet近似逆行列前処理の高速化2007

    • Author(s)
      今倉暁, 曽我部知広, 他
    • Journal Title

      日本応用数理学会論文誌 17

      Pages: 523-542

    • Related Report
      2008 Final Research Report 2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Bi-CR法への準最小残差アプローチの適用について2007

    • Author(s)
      南さつき, 曽我部知広, 他
    • Journal Title

      日本応用数理学会論文誌 17

      Pages: 301-317

    • Related Report
      2008 Final Research Report 2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 非対称行列用共役残差法に基づく積型反復解法2007

    • Author(s)
      阿部邦美, 曽我部知広, 他
    • Journal Title

      情報処理学会論文誌「コンピューティングシステム」 48

      Pages: 11-21

    • NAID

      110006274058

    • Related Report
      2008 Final Research Report 2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On a two-term recurrence for the determinant of a general matrix2007

    • Author(s)
      T. Sogabe
    • Journal Title

      Applied Mathematics and Computation 187

      Pages: 785-788

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 非対称行列用共役残差法に基づく積型反復解法2007

    • Author(s)
      阿部邦美, 曽我部知広, 藤野清次, 張紹良
    • Journal Title

      2007年ハイパフォーマンスコンピューティングと計算科学シンポジウム論文集 Vol.2007 No. 1

      Pages: 17-24

    • NAID

      110006274058

    • Related Report
      2006 Annual Research Report
  • [Journal Article] A COCR method for solving complex symmetric linear systems2007

    • Author(s)
      T.Sogabe, S.-L.Zhang
    • Journal Title

      Journal of Computational and Applied Mathematics Vol.199

      Pages: 297-303

    • Related Report
      2006 Annual Research Report
  • [Journal Article] CRS: a fast algorithm based on Bi-CR for solving nonsvmmeric linear systems2006

    • Author(s)
      T. Sogabe, S. -L. Zhang
    • Journal Title

      Hokkaido University Technical Report Series in Mathematics Vol.112

      Pages: 15-18

    • Related Report
      2008 Final Research Report
  • [Journal Article] CRS : a fast algorithm based on Bi-CR for solving nonsvmmeric linear systems2006

    • Author(s)
      T.Sogabe, S.-L.Zhang
    • Journal Title

      Hokkaido University Technical Report Series in Mathematics Vol.112

      Pages: 15-18

    • Related Report
      2006 Annual Research Report
  • [Presentation] A fast solver for generalized shifted linear systems with complex symmetric matrices2009

    • Author(s)
      T. Sogabe, S. -L. Zhang
    • Organizer
      The 7th International Conference on Numerical Optimization and Numerical Linear Algebra
    • Place of Presentation
      麗江, 雲南省, 中国
    • Year and Date
      2009-08-16
    • Related Report
      2008 Final Research Report
  • [Presentation] A fast solver for generalized shifted linear systems with complex symmetric matrices2009

    • Author(s)
      T.Sogabe, S.-L.Zhang
    • Organizer
      The 7th International Conference on Numerical Optimization and Numerical Linear Algebra
    • Place of Presentation
      Lijiang, Yunnan, China
    • Related Report
      2008 Annual Research Report
  • [Presentation] Numerical Algorithms for Solving Shifted Complex Symmetric Linear Systems2008

    • Author(s)
      S. -L. Zhang, T. Sogabe
    • Organizer
      The NIMS 2008 Conference & The 4th East Asia SIAM Conference
    • Place of Presentation
      デジョン, 韓国
    • Year and Date
      2008-10-10
    • Related Report
      2008 Final Research Report
  • [Presentation] Extra large size linear problem solver and its application to the excitation spectra in the many-electron problem2008

    • Author(s)
      S. Yamamoto, T. Sogabe, T. Hoshi, S. -L. Zhang, T. Fujiwara
    • Organizer
      International Conference on Quantum Simulators and Design
    • Place of Presentation
      日本科学未来館, 東京
    • Year and Date
      2008-05-31
    • Related Report
      2008 Final Research Report
  • [Presentation] Implicit wavelet sparse approximate inverse preconditioner using blocked finger pattern for nonsymmetric linear systems2008

    • Author(s)
      A. Imakura, T. Sogabe, S. -L. Zhang
    • Organizer
      ALA 2008 Applied Linear Algebra-in honor of Ivo Marek.
    • Place of Presentation
      ノビサド, セルビア
    • Year and Date
      2008-04-28
    • Related Report
      2008 Final Research Report
  • [Presentation] Implicit wavelet sparse approximate inverse preconditioner using blocked finger pattern for nonsymmetric linear systems2008

    • Author(s)
      A.Imakura, T.Sogabe, S.-L.Zhang
    • Organizer
      ALA 2008 Applied Linear Algebra-in honor of Ivo Marek
    • Place of Presentation
      Novi Sad, Serbia
    • Related Report
      2008 Annual Research Report
  • [Presentation] Extra large size linear problem solver and its application to the excitation spectra in the many-electron problem2008

    • Author(s)
      S.Yamamoto, T.Sogabe, T.Hoshi, S.-L.Zhang, T.Fujiwara
    • Organizer
      International Conference on Quantum Simulators and Design 2008-
    • Place of Presentation
      東京 日本科学未来館
    • Related Report
      2008 Annual Research Report
  • [Presentation] Numerical agorithms for solving shifted complex symmetric linear systems2008

    • Author(s)
      S.-L.Zhang, T.Sogabe
    • Organizer
      The NIMS 2008 Conference & The 4th East Asia SIAM Conference
    • Place of Presentation
      Daejeon, Korea
    • Related Report
      2008 Annual Research Report
  • [Presentation] On a weighted quasi-residual minimization strategy of QMR for solving complex symmetric shifted linear systems2007

    • Author(s)
      T. Sogabe, S. -L. Zhang
    • Organizer
      Harrachov 2007-Computational Methods with Applications-.
    • Place of Presentation
      ハラホフ, チェコ
    • Year and Date
      2007-08-24
    • Related Report
      2008 Final Research Report
  • [Presentation] On a weighted quasi-residual minimization strategy of QMR for solving complex symmetric shifted linear systems2007

    • Author(s)
      T. Sogabe, S.-L. Zhang
    • Organizer
      Harrachov 2007-Computational Methods with Applications-
    • Place of Presentation
      ハラホフ,チェコ
    • Year and Date
      2007-08-24
    • Related Report
      2007 Annual Research Report
  • [Presentation] 陰的wavelet近似逆行列前処理のFinger Patternに対するブロック化技法について2007

    • Author(s)
      今倉暁, 曽我部知広, 張紹良
    • Organizer
      第36回数値解析シンポジウム
    • Place of Presentation
      ウェルシティ湯河原
    • Year and Date
      2007-06-21
    • Related Report
      2008 Final Research Report
  • [Presentation] 陰的wavelet近似逆行列前処理のFinger Patternに対するブロック化技法について,2007

    • Author(s)
      今倉暁, 曽我部知広, 張紹良
    • Organizer
      第36回数値解析シンポジウム
    • Place of Presentation
      ウェルシティ湯河原
    • Year and Date
      2007-06-21
    • Related Report
      2007 Annual Research Report
  • [Remarks]

    • URL

      http://www.aichi-pu.ac.jp/ist/person/sogabe/sogabe.html

    • Related Report
      2008 Final Research Report

URL: 

Published: 2006-04-01   Modified: 2016-04-21  

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