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

• Project/Area Number: 19560065
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Engineering fundamentals
• Research Institution: Nagoya University
• Principal Investigator: ZHANG Shao-Liang (ZHANG Shao-liang) Nagoya University, 大学院・工学研究科, 教授 (20252273)
• Co-Investigator(Kenkyū-buntansha): 山本 有作 神戸大学, 大学院・工学研究科, 教授 (20362288) ; 曽我部 知広 愛知県立大学, 大学院・情報科学研究科, 准教授 (30420368) ; 阿部 邦美 岐阜聖徳学園大学, 経済情報学部, 准教授 (10311086)
• Project Period (FY): 2007 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000); Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2007: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
• 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

• [Journal Article] A novel algorithm of large-scale simultaneous linear equations (2010)
  • 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] Performance Modeling of Multishift QR Algorithms for the Parallel Solution of Symmetric Tridiagonal Eigenvalue Problems (2010)
  • Author(s): T.Miyata, Y.Yamamoto, S.-L.Zhang
  • Journal Title: Lecture Notes in Computer Science Volume: 6082 Pages: 401-412
• [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 Volume: 20 Pages: 115-129
  • Peer Reviewed
• [Journal Article] A novel algorithm of large-scale simultaneous linear equations (2010)
  • Author(s): T.Fujiwara, T.Hoshi, S.Yamamoto, T.Sogabe, S.-L.Zhang
  • Journal Title: J.Phys.: Condens.Matter Volume: 22, 074206 Pages: 1-6
  • 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 systems (2009)
  • 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] 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 19巻 Pages: 537-550
  • 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 19巻 Pages: 551-564
  • Peer Reviewed
• [Journal Article] An extension of the conjugate residual method to nonsymmetric linear systems (2009)
  • Author(s): T. Sogabe, M. Sugihara, S.-L. Zhang
  • Journal Title: J.Comput.Appl.Math 226巻 Pages: 103-113
  • 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 19 Pages: 537-550
  • 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 19 Pages: 551-564
  • Peer Reviewed
• [Journal Article] An extension of the conjugate residual method to nonsymmetric linear systems (2009)
  • Author(s): T.Sogabe, M.Sugihara, S.-L..Zhang
  • Journal Title: J. Comput. Appl. Math. 226 Pages: 103-113
  • 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 19 Pages: 293-312
  • 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 model (2008)
  • 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 systems (2008)
  • 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] On a weighted quasi-residual minimization strategy for solving complex symmetric shifted linear systems (2008)
  • Author(s): T. Sogabe, T. Hoshi, S.-L. Zhang, T. Fujiwara
  • Journal Title: Electron.Trans.Numer.Anal 31巻 Pages: 126-140
  • Peer Reviewed
• [Journal Article] Shifted COCG method and its application to double orbital extended Hubbard model (2008)
  • Author(s): S. Yamamoto, T. Sogabe, T. Hoshi, S.-L. Zhang, T. Fujiwara
  • Journal Title: J.Phys.Soc.Jpn 77巻 Pages: 1-8
  • 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 18巻 Pages: 155-170
  • 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 18巻 Pages: 563-577
  • Peer Reviewed
• [Journal Article] On a weighted quasi-residual minimization strategy for solving complex symmetric shifted linear systems (2008)
  • Author(s): T.Sogabe, T.Hoshi, S.-L.Zhang, T.Fujiwara
  • Journal Title: Electron.Trans.Numer.Anal. 31 Pages: 126-140
  • Peer Reviewed
• [Journal Article] Shifted COCG method and its application to double orbital extended Hubbard model (2008)
  • Author(s): S.Yamamoto, T.Sogabe, T.Hoshi, S.-L.Zhang, T.Fujiwara
  • Journal Title: J.Phys.Soc.Jpn. 77 Pages: 1-8
  • 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 18 Pages: 155-170
  • 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 18 Pages: 563-577
  • 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 systems (2007)
  • 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] A COCR method for solving complex symmetric linear systems (2007)
  • Author(s): T. Sogabe, S.-L. Zhang
  • Journal Title: J.Computational and Applied Mathematics 199巻 Pages: 297-303
  • 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 17-4巻 Pages: 523-542
  • Peer Reviewed
• [Journal Article] A COCR method for solving complex symmetric linear systems (2007)
  • Author(s): T. Sogabe and S.-L. Zhang
  • Journal Title: J. Computatioal and Applied Mathematics 199 Pages: 297-303
  • 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 17-3 Pages: 301-317
  • 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 17-4 Pages: 523-542
  • Peer Reviewed
• [Journal Article]
  • Peer Reviewed
• [Journal Article]
  • Peer Reviewed
• [Journal Article]
  • Peer Reviewed
• [Presentation] A Projection Approach Based on the Residue Theorem for Eigenvalues within a Multiply Connected Domain (2010)
  • 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.
• [Presentation] A Look-Back Technique of Restart for the GMRES(m) Method (2010)
  • 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.
• [Presentation] GMRES(m) Method with Look-Back-type Restart for Solving Nonsymmetric Linear Systems (2010)
  • 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.
• [Presentation] A Block IDR(s) method for linear systems with multiple right-hand sides (2010)
  • 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.
• [Presentation] An Approach to Automatic Tuning for the Parallel Householder QR decomposition (2010)
  • Author(s): T.Fukaya, Y.Yamamoto, S.-L.Zhang
  • Organizer: SIAM Conference on Parallel Processing for Scientific Computing (PP10)
  • Place of Presentation: Seattle USA.
• [Presentation] GMRES(m) method with Look-Back-type restart for solving nonsymmetric linear systems (2010)
  • Author(s): S.-L.Zhang, A.Imakura, T.Sogabe
  • Organizer: 7th International Conference on Scientific Computing and Applications
  • Place of Presentation: Dalian, China
• [Presentation] A Numerical Method Based on the Residue Theorem for Computing Eigenvalues in Multiply Connected Region (2009)
  • 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] A fast iterative method for solving generalized shifted linear systems with complex symmetric matrices (2009)
  • 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
• [Presentation] Large-scale electronic structure calculations and nanomaterial process (2009)
  • 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
• [Presentation] A Dynamic Programming Approach to Performance Optimization for the QR Decomposition (2009)
  • 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
• [Presentation] A look-back strategy for the GMRES(m) method (2009)
  • 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.
• [Presentation] Computation of eigenvalues in multiply connected region (2009)
  • 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.
• [Presentation] A fast solver for generalized shifted linear systems with complex symmetric matrices (2009)
  • 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.
• [Presentation] A Dynamic Programming Approach to Optimizing the Blocking Strategy for the Householder QR Decompositio (2009)
  • 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.
• [Presentation] A New Variant of the GMRES(m) Method for Solving Nonsymmetric Linear Systems (2009)
  • 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.
• [Presentation] An approach to fast solution of generalized shifted linear systems with complex symmetric matrices (2009)
  • Author(s): T.ogabe, S.-L.Zhang
  • Organizer: Numerical Analysis and Scientific Computing with Applications (NASCA2009)
  • Place of Presentation: Agadir Morocco
• [Presentation] An efficient variant of the GMRES(m) method based on error equations (2009)
  • Author(s): A.Imakura, T.Sogabe, S.-L.Zhang
  • Organizer: Numerical Analysis and Scientific Computing with Applications (NASCA2009)
  • Place of Presentation: Agadir Morocco.
• [Presentation] A New Variant of the GMRES(m)Method for Solving Nonsymmetric Linear Systems (2009)
  • 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
• [Presentation] A Dynamic Programming Approach to Optimizing the Blocking Strategy for the Householder QR Decomposition (2008)
  • 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 Systems (2008)
  • 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] Numerical Algorithms for Solving Shifted Complex Symmetric Linear Systems (2008)
  • Author(s): S.-L.Zhang, T.Sogabe
  • Organizer: The NIMS 2008 Conference & The 4th East Asia SIAM Conference
  • Place of Presentation: Daejeon, Korea.
• [Presentation] An Efficient Parallelization of the QR Algorithm for Symmetric Tridiagonal Eigenproblems (2008)
  • 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
• [Presentation] A Large-Grained Parallel Algorithm for Nonlinear Eigenvalue Problems and Its Implementation Using OmniRPC (2008)
  • Author(s): T.Amako, Y.Yamamoto, S.-L.Zhang
  • Organizer: Cluster 2008
  • Place of Presentation: Tsukuba.
• [Presentation] A Large-Grained Parallel Algorithm for Nonlinear Eigenvalue Problems Using Complex Contour Integration (2008)
  • Author(s): T.Amako, Y.Yamamoto, S.-L.Zhang
  • Organizer: PARA 2008
  • Place of Presentation: Trondheim Norway.
• [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.
• [Presentation] Performance of the Complex Hessenberg QR Algorithm on the CSX600 Processor (2008)
  • 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.
• [Presentation] Numerical Algorithms for Solving Shifted Complex Symmetric Linear Systems (2008)
  • Author(s): S.-L.Zhang, T.Sogabe
  • Organizer: The NIMS 2008 Conference & The 4th East Asia SIAM Conference
  • Place of Presentation: Daejeon, Korea
• [Presentation] QR Algorithm for the Parallel Solution of Symmetric Tridiagonal Eigenproblem (2007)
  • 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
• [Presentation] On a weighted quasi-residual minimization strategy of QMR for solving complex symmetric shifted linear systems (2007)
  • Author(s): T.Sogabe, S.-L.Zhang
  • Organizer: Harrachov2007-Computational Methods with Applications
  • Place of Presentation: Harrachov, Czech Republic.
• [Presentation] Krylov subspace methods for solving complex symmetric shifted linear systems (2007)
  • 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.
• [Presentation] Sparse approximate inverse preconditioners for complex symmetric systems of linear equations (2007)
  • 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.
• [Presentation] Krylov eubspace methods for solving complex symmetric shifted linear systems (2007)
  • Author(s): T. Sogabe, T. Hoshi, S.-L. Zhang, and T. Fujiwara
  • Organizer: The 6th International Congress on Industrial and Applied Mathematics
  • Place of Presentation: Zurich, Switzerland
• [Remarks]
  • URL: http://kenpro.mynu.jp:8001/Profiles/0033/0003382/profile.html
• [Remarks]
  • URL: http://kenpro.mynu.jp:8001/Profiles/0033/0003382/profile.html