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2010 Fiscal Year Final Research Report

A study on fast solvers for large linear systems in the field of scientific computations

Research Project

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Project/Area Number 19560065
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Engineering fundamentals
Research InstitutionNagoya University

Principal Investigator

ZHANG Shao-Liang  Nagoya University, 大学院・工学研究科, 教授 (20252273)

Project Period (FY) 2007 – 2010
Keywords線形方程式 / 高速解法 / 計算サーバ / 計算科学 / クリロフ部分空間法
Research Abstract

There are many researches about Krylov subspace methods for large linear systems and some research results were utilized for solving practical problems. However, these results can be used for some special cases. We studied and developed fast solvers for large linear systems in the field of scientific computations.

  • Research Products

    (44 results)

All 2010 2009 2008 2007 Other

All Journal Article (16 results) (of which Peer Reviewed: 16 results) Presentation (28 results)

  • [Journal Article] A novel algorithm of large-scale simultaneous linear equations2010

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

      J.Phys. : Condens.Matter Vol.22

      Pages: 1-6

    • Peer Reviewed
  • [Journal Article] Jacobi-Davidson 法における修正方程式の解法-射影空間における Krylov 部分空間のシフト不変性に基づいて-2010

    • Author(s)
      宮田考史, 曽我部知広, 張紹良
    • Journal Title

      日本応用数理学会論文誌 Vol.20

      Pages: 115-129

    • Peer Reviewed
  • [Journal Article] 行列の指数関数に基づく連立線形常微分方程式の大粒度並列化解法とその評価2009

    • Author(s)
      則竹渚宇, 今倉暁, 山本有作, 張紹良
    • Journal Title

      日本応用数理学会論文誌 Vol.19

      Pages: 293-312

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

    • Author(s)
      曽我部知広, 杉原正顯, 張紹良
    • Journal Title

      J.Comput.Appl.Math Vol.226

      Pages: 103-113

    • Peer Reviewed
  • [Journal Article] GMRES(m)法のリスタートについて2009

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

      日本応用数理学会論文誌 Vol.19

      Pages: 551-564

    • Peer Reviewed
  • [Journal Article] 多重連結領域の固有値問題に対する Sakurai-Sugiura 法の拡張2009

    • Author(s)
      宮田考史, 杜磊, 曽我部知広, 山本有作, 張紹良
    • Journal Title

      日本応用数理学会論文誌 Vol.19

      Pages: 537-550

    • Peer Reviewed
  • [Journal Article] 対称三重対角行列向けマルチシフトQR 法の漸近的収束性解析2008

    • Author(s)
      宮田考史, 岩崎雅史, 山本有作, 張紹良
    • Journal Title

      日本応用数理学会論文誌 Vol.18

      Pages: 563-577

    • 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, 阿部邦美, 曽我部知広, 張紹良
    • Journal Title

      日本応用数理学会論文誌 Vol.18

      Pages: 155-170

    • 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 Vol.77

      Pages: 1-8

    • 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 Vol.31

      Pages: 126-140

    • 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, 張紹良
    • Journal Title

      日本応用数理学会論文誌 Vol.17

      Pages: 523-542

    • 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, 杉原正顯, 張紹良
    • Journal Title

      日本応用数理学会論文誌 Vol.17

      Pages: 301-317

    • Peer Reviewed
  • [Journal Article] A COCR method for solving complex symmetric linear systems2007

    • Author(s)
      曽我部知広, 張紹良
    • Journal Title

      J.Computational and Applied Mathematics Vol.199

      Pages: 297-303

    • Peer Reviewed
  • [Journal Article]

    • Peer Reviewed
  • [Journal Article]

    • Peer Reviewed
  • [Journal Article]

    • Peer Reviewed
  • [Presentation] A Block IDR(s) method for linear systems with multiple right-hand sides2010

    • Author(s)
      L.Du, T.Sogabe, Y.Yamamoto, B.Yu, S.-L.Zhang
    • Organizer
      11th Copper Mountain Conference on Iterative methods, Copper Mountain
    • Place of Presentation
      Colorado, USA.
    • Year and Date
      20101104-20101109
  • [Presentation] A Projection Approach Based on the Residue Theorem for Eigenvalues within a Multiply Connected Domain2010

    • Author(s)
      S.-L.Zhang, T.Miyata, L.Du, T.Sogabe, Y.Yamamoto
    • Organizer
      The Third China-Japan-Korea Joint Conference on Numerical Mathematics
    • Place of Presentation
      Gangneung, Korea.
    • Year and Date
      20101019-20101023
  • [Presentation] A Look-Back Technique of Restart for the GMRES(m) Method2010

    • Author(s)
      A.Imakura, T.Sogabe, S.-L.Zhang
    • Organizer
      Applied Linear Algebra - in honor of Hans Schneider, University of Novi Sad
    • Place of Presentation
      Novi Sad, Serbia.
    • Year and Date
      20100624-20100628
  • [Presentation] GMRES(m) Method with Look-Back-type Restart for Solving Nonsymmetric Linear Systems2010

    • Author(s)
      S.-L.Zhang, A.Imakura, T.Sogabe
    • Organizer
      The 7th International Conference on Scientific Computing and Application
    • Place of Presentation
      Dalian P.R., China.
    • Year and Date
      20100613-20100616
  • [Presentation] An Approach to Automatic Tuning for the Parallel Householder QR decomposition2010

    • Author(s)
      T.Fukaya, Y.Yamamoto, S.-L.Zhang
    • Organizer
      SIAM Conference on Parallel Processing for Scientific Computing (PP10)
    • Place of Presentation
      Seattle USA.
    • Year and Date
      20100224-20100226
  • [Presentation] A fast iterative method for solving generalized shifted linear systems with complex symmetric matrices2009

    • Author(s)
      T.Sogabe, T.Hoshi, S.-L.Zhang, T.Fujiwara
    • Organizer
      International Symposium of Electronic Structure Calculations -Theory, Correlated and Large Scale Systems and Numerical Methods-
    • Place of Presentation
      Tokyo
    • Year and Date
      20091107-20091109
  • [Presentation] Large-scale electronic structure calculations and nanomaterial process2009

    • Author(s)
      T.Hoshi, S.Yamamoto, T.Sogabe, S.-L.Zhang, S.Nishino, H.Teng, T.Fujiwara
    • Organizer
      International Symposium of Electronic Structure Calculations -Theory, Correlated and Large Scale Systems and Numerical Methods-
    • Place of Presentation
      Tokyo
    • Year and Date
      20091107-20091109
  • [Presentation] A Dynamic Programming Approach to Performance Optimization for the QR Decomposition2009

    • Author(s)
      T.Fukaya, T.Sogabe, S.-L.Zhang
    • Organizer
      International Symposium of Electronic Structure Calculations -Theory, Correlated and Large Scale Systems and Numerical Methods-
    • Place of Presentation
      Tokyo
    • Year and Date
      20091107-20091109
  • [Presentation] A look-back strategy for the GMRES(m) method2009

    • Author(s)
      A.Imakura, T.Sogabe, S.-L.Zhang
    • Organizer
      The 7th International Conference on Numerical Optimization and Numerical Linear Algebra
    • Place of Presentation
      Lijiang, Yunnan, China.
    • Year and Date
      20090816-20090819
  • [Presentation] Computation of eigenvalues in multiply connected region2009

    • Author(s)
      T.Miyata, L.Du, T.Sogabe, Y.Yamamoto, S.-L.Zhang
    • Organizer
      The 7th International Conference on Numerical Optimization and Numerical Linear Algebra
    • Place of Presentation
      Lijiang, Yunnan, China.
    • Year and Date
      20090816-20090819
  • [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.
    • Year and Date
      20090816-20090819
  • [Presentation] A Dynamic Programming Approach to Optimizing the Blocking Strategy for the Householder QR Decompositio2009

    • Author(s)
      T.Fukaya, Y.Yamamoto, S.-L.Zhang
    • Organizer
      The 2nd International Conference on Mathematical Modelling and Computation and The 5th East Asia SIAM Conference
    • Place of Presentation
      Universiti Brunei Darussalam, Brunei.
    • Year and Date
      20090608-20090611
  • [Presentation] A New Variant of the GMRES(m) Method for Solving Nonsymmetric Linear Systems2009

    • Author(s)
      S.-L.Zhang, A.Imakura, T.Sogabe
    • Organizer
      The 2nd International Conference in Mathematical Modelling and Computation and The 5th East Asia SIAM Conference
    • Place of Presentation
      Universiti Brunei Darussalam, Brunei.
    • Year and Date
      20090608-20090611
  • [Presentation] An approach to fast solution of generalized shifted linear systems with complex symmetric matrices2009

    • Author(s)
      T.ogabe, S.-L.Zhang
    • Organizer
      Numerical Analysis and Scientific Computing with Applications (NASCA2009)
    • Place of Presentation
      Agadir Morocco
    • Year and Date
      20090518-20090522
  • [Presentation] An efficient variant of the GMRES(m) method based on error equations2009

    • Author(s)
      A.Imakura, T.Sogabe, S.-L.Zhang
    • Organizer
      Numerical Analysis and Scientific Computing with Applications (NASCA2009)
    • Place of Presentation
      Agadir Morocco.
    • Year and Date
      20090518-20090522
  • [Presentation] A Numerical Method Based on the Residue Theorem for Computing Eigenvalues in Multiply Connected Region2009

    • Author(s)
      T.Miyata, L.Du, T.Sogabe, Y.Yamamoto, S.-L.Zhang
    • Organizer
      SIAM Conference on Applied Linear Algebra
    • Place of Presentation
      Monterey USA.
    • Year and Date
      2009-10-28
  • [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
      Daejeon, Korea.
    • Year and Date
      20081010-20081012
  • [Presentation] An Efficient Parallelization of the QR Algorithm for Symmetric Tridiagonal Eigenproblems2008

    • Author(s)
      T.Miyata, Y.Yamamoto, S.-L.Zhang
    • Organizer
      The NIMS 2008 Conference & The 4th East Asia SIAM Conference
    • Place of Presentation
      Daejeon Korea
    • Year and Date
      20081010-20081012
  • [Presentation] A Large-Grained Parallel Algorithm for Nonlinear Eigenvalue Problems and Its Implementation Using OmniRPC2008

    • Author(s)
      T.Amako, Y.Yamamoto, S.-L.Zhang
    • Organizer
      Cluster 2008
    • Place of Presentation
      Tsukuba.
    • Year and Date
      20080929-20081001
  • [Presentation] A Large-Grained Parallel Algorithm for Nonlinear Eigenvalue Problems Using Complex Contour Integration2008

    • Author(s)
      T.Amako, Y.Yamamoto, S.-L.Zhang
    • Organizer
      PARA 2008
    • Place of Presentation
      Trondheim Norway.
    • Year and Date
      20080513-20080516
  • [Presentation] Performance of the Complex Hessenberg QR Algorithm on the CSX600 Processor2008

    • Author(s)
      T.Miyata, Y.Yamamoto, S.-L.Zhang, Y.Nakamura
    • Organizer
      SIAM Conference on Parallel Processing for Scientific Computing 2008
    • Place of Presentation
      Atlanta GA, USA.
    • Year and Date
      20080512-20080514
  • [Presentation] Implicit wavelet sparse approximate inverse preconditioner using blocked finger pattern for nonsymmetric linear systems(Winner among young researchers)2008

    • Author(s)
      A.Tmakura, T.Sogabe, S.-L.Zhang
    • Organizer
      ALA 2008 Applied Linear Algebra-in honor of Tvo Marek
    • Place of Presentation
      Novi Sad Serbia.
    • Year and Date
      20080428-20080430
  • [Presentation] A Dynamic Programming Approach to Optimizing the Blocking Strategy for the Householder QR Decomposition2008

    • Author(s)
      T.Fukaya, Y.Yamamoto, S.-L.Zhang
    • Organizer
      iWAPT 2008
    • Place of Presentation
      Tsukuba.
    • Year and Date
      2008-10-01
  • [Presentation] Block Algorithms of Implicit Wavelet Sparse Approximate Inverse Preconditioner for Nonsymmetric Linear Systems2008

    • Author(s)
      A.Imakura, T.Sogabe, S.-L.Zhang
    • Organizer
      Nagoya-COE and Beijing-LHD Joint Workshopon "Frontier of Computational Science"
    • Place of Presentation
      Nagoya University
    • Year and Date
      2008-05-24
  • [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
      Harrachov2007-Computational Methods with Applications
    • Place of Presentation
      Harrachov, Czech Republic.
    • Year and Date
      20070819-20070825
  • [Presentation] Krylov subspace methods for solving complex symmetric shifted linear systems2007

    • Author(s)
      T.Sogabe, T.Hoshi, S.-L.Zhang, T.Fujiwara
    • Organizer
      The 6th International Congress on Industrial and Applied Mathematics
    • Place of Presentation
      Zurich, Switzerland.
    • Year and Date
      20070716-20070720
  • [Presentation] Sparse approximate inverse preconditioners for complex symmetric systems of linear equations2007

    • Author(s)
      T.Sogabe, S.-L.Zhang
    • Organizer
      2007 International Conference on Preconditioning Techniques for Large Sparse Matrix Problems in Scientific and Industrial Applications (Precond 2007)
    • Place of Presentation
      Toulouse, France.
    • Year and Date
      20070716-20070720
  • [Presentation] QR Algorithm for the Parallel Solution of Symmetric Tridiagonal Eigenproblem2007

    • Author(s)
      T.Miyata, Y.Yamamoto, S.-L.Zhang
    • Organizer
      Beijing-LIID and Nagoya-COE Joint Workshop on "Frontier of Computational Science
    • Place of Presentation
      Beijing Cnian
    • Year and Date
      2007-02-18

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Published: 2012-01-26   Modified: 2016-04-21  

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