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Developments of iterative-type preconditioning techniques for large linear systems and their application

Research Project

Project/Area Number 25870099
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Computational science
High performance computing
Research InstitutionUniversity of Tsukuba

Principal Investigator

Imakura Akira  筑波大学, システム情報系, 助教 (60610045)

Project Period (FY) 2013-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords高性能計算 / 数値解析 / 大規模連立一次方程式 / 反復法 / 前処理技術
Outline of Final Research Achievements

In this project, we aim to develop efficient algorithms for solving large linear systems and apply to some real applications. In order to achieve these purposes, we developed iterative-type preconditioning techniques which have high speed, high stability and high parallel efficiency. We also provided parameters optimization techniques for improving convenience of the proposed preconditioning techniques.
The proposed preconditioning techniques and their parameter optimization techniques were applied to supernova simulation. The proposed techniques made it possible to solve efficiently difficult problems for traditional techniques. Then, the proposed techniques adopted to a supernova simulation code and are beginning to make achievements.

Report

(4 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (46 results)

All 2016 2015 2014 2013 Other

All Journal Article (12 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 11 results,  Open Access: 5 results,  Acknowledgement Compliant: 5 results) Presentation (32 results) (of which Int'l Joint Research: 8 results,  Invited: 3 results) Remarks (2 results)

  • [Journal Article] Error bounds of Rayleigh--Ritz type contour integral-based eigensolver for solving generalized eigenvalue problems2016

    • Author(s)
      Akira Imakura, Lei Du, Tetsuya Sakurai
    • Journal Title

      Numerical Algorithms

      Volume: 71 Pages: 103-120

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Recovering from accuracy deterioration in the contour integral-based eigensolver2016

    • Author(s)
      Tetsuya Hasegawa, Akira Imakura, Tetsuya Sakurai
    • Journal Title

      JSIAM Letters

      Volume: 8 Issue: 0 Pages: 1-4

    • DOI

      10.14495/jsiaml.8.1

    • NAID

      130005125234

    • ISSN
      1883-0609, 1883-0617
    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Improving the convergence behaviour of BiCGSTAB by applying <i>D</i>-norm minimization2015

    • Author(s)
      Lijiong Su, Akira Imakura, Hiroto Tadano, Tetsuya Sakurai
    • Journal Title

      JSIAM Letters

      Volume: 7 Issue: 0 Pages: 37-40

    • DOI

      10.14495/jsiaml.7.37

    • NAID

      130005068708

    • ISSN
      1883-0609, 1883-0617
    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Filter analysis for the stochastic estimation of eigenvalue counts2015

    • Author(s)
      Yasuyuki Maeda, Yasunori Futamura, Akira Imakura, Tetsuya Sakurai
    • Journal Title

      JSIAM Letters

      Volume: 7 Issue: 0 Pages: 53-56

    • DOI

      10.14495/jsiaml.7.53

    • NAID

      130005087644

    • ISSN
      1883-0609, 1883-0617
    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Improvement of the accuracy of the approximate solution of the Block BiCR method2014

    • Author(s)
      H. Tadano, Y. Ishikawa, and A. Imakura
    • Journal Title

      JSIAM Letters

      Volume: 6 Issue: 0 Pages: 61-64

    • DOI

      10.14495/jsiaml.6.61

    • NAID

      130004706457

    • ISSN
      1883-0609, 1883-0617
    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Development of the Block BiCGSTAB($\ell$) method for solving linear systems with multiple right hand sides2014

    • Author(s)
      S. Saito, H. Tadano, and A. Imakura
    • Journal Title

      JSIAM Letters

      Volume: 6 Issue: 0 Pages: 65-68

    • DOI

      10.14495/jsiaml.6.65

    • NAID

      130004706458

    • ISSN
      1883-0609, 1883-0617
    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] An efficient algorithm to construct an orthonormal basis for the extended Krylov subspace2014

    • Author(s)
      Akira Imakura
    • Journal Title

      East Asian Journal on Applied Mathematics

      Volume: 4 Issue: 3 Pages: 267-282

    • DOI

      10.4208/eajam.240413.020614a

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] A block Arnoldi-type contour integral spectral projection method for solving generalized eigenvalue problems2014

    • Author(s)
      Akira Imakura, Lei Du, Tetsuya Sakurai
    • Journal Title

      Applied Mathematics Letters

      Volume: 32 Pages: 22-27

    • DOI

      10.1016/j.aml.2014.02.007

    • Related Report
      2013 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] A Weighted Block GMRES method for solving linear systems with multiple right-hand sides2013

    • Author(s)
      Akira IMAKURA, Lei DU, Hiroto TADANO
    • Journal Title

      JSIAM Letters

      Volume: 5 Issue: 0 Pages: 65-68

    • DOI

      10.14495/jsiaml.5.65

    • NAID

      130003385510

    • ISSN
      1883-0609, 1883-0617
    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] 残差最小性に基づくKrylov部分空間反復法に対する疎行列用直接解法を用いた前処理のパラメータ推定2013

    • Author(s)
      山崎 育朗, 今倉 暁, 多田野 寛人, 櫻井 鉄也
    • Journal Title

      日本応用数理学会論文誌

      Volume: 23 Pages: 381-404

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] An Efficient Variant of the Restarted Shifted GMRES Method for Solving Shifted Linear Systems2013

    • Author(s)
      Akira IMAKURA, Tomohiro SOGABE and Shao-Liang ZHANG
    • Journal Title

      Journal of Mathematical Research with Applications

      Volume: 33 Pages: 127-141

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] 重み付き定常反復型前処理のためのパラメータ最適化手法および超新星爆発計算における有効性2013

    • Author(s)
      今倉 暁, 櫻井 鉄也, 住吉 光介, 松古 栄夫
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1848 Pages: 15-24

    • Related Report
      2013 Research-status Report
  • [Presentation] 2つのKrylov部分空間を利用した複素モーメント型固有値解法2016

    • Author(s)
      今倉 暁, 櫻井 鉄也
    • Organizer
      日本応用数理学会 第12回 研究部会連合発表会
    • Place of Presentation
      神戸学院大学 ポートアイランドキャンパス(兵庫県神戸市)
    • Year and Date
      2016-03-04
    • Related Report
      2015 Annual Research Report
  • [Presentation] Krylov subspace in complex moment-based eigensolver2016

    • Author(s)
      Akira Imakura,
    • Organizer
      Workshop on Numerical Algebra, Algorithms, and Analysis
    • Place of Presentation
      National Institute of Informatics (NII), Tokyo, Japan (東京都千代田区)
    • Year and Date
      2016-01-11
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] A novel complex moment-based eigensolver using a communication-avoiding Arnoldi process2015

    • Author(s)
      Akira Imakura, Tetsuya Sakurai
    • Organizer
      SIAM Conference on Applied Linear Algebra (SIAM LA15)
    • Place of Presentation
      Hyatt Regency Atranta, Atranta, Georgia, USA
    • Year and Date
      2015-10-26
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] A Contour Integral-based Parallel Eigensolver with Higher Complex Moments2015

    • Author(s)
      Tetsuya Sakurai, Yasunori Futamura, Akira Imakura
    • Organizer
      SIAM Conference on Applied Linear Algebra (SIAM LA15)
    • Place of Presentation
      Hyatt Regency Atranta, Atranta, Georgia, USA
    • Year and Date
      2015-10-26
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Development of the Shifted Block BiCGGR method and accuracy improvement of approximate solutions2015

    • Author(s)
      Hiroto Tadano, Shusaku Saito, Akira Imakura
    • Organizer
      International Conference on Simulation Technology (JSST2015)
    • Place of Presentation
      Toyama International Conference Center (富山県富山市)
    • Year and Date
      2015-10-12
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 複数右辺ベクトル・複数シフトをもつ線形方程式に対するShifted Block Krylov部分空間法の近似解の精度改善2015

    • Author(s)
      多田野 寛人, 齋藤 周作, 今倉 暁
    • Organizer
      【プラズマ壁相互作用における非線形現象の理論モデル構築と画像・動画解析手法開発に関する研究会】第1回非線形・可視化部門研究会
    • Place of Presentation
      核融合科学研究所(岐阜県土岐市)
    • Year and Date
      2015-09-28
    • Related Report
      2015 Annual Research Report
  • [Presentation] Error resilience strategy of a complex moment-based eigensolver2015

    • Author(s)
      Akira Imakura, Yasunori Futamura, Tetsuya Sakurai
    • Organizer
      International Workshop on Eigenvalue Problems: Algorithms; Software and Applications, in Petascale Computing (EPASA2015)
    • Place of Presentation
      EPOCHAL TSUKUBA, Tsukuba-city, Japan (茨城県つくば市)
    • Year and Date
      2015-09-14
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Accuracy improvement of the Shifted Block BiCGGR method for linear systems with multiple shifts and multiple right-hand sides2015

    • Author(s)
      Hiroto Tadano, Shusaku Saito, Akira Imakura
    • Organizer
      International Workshop on Eigenvalue Problems: Algorithms; Software and Applications, in Petascale Computing (EPASA2015)
    • Place of Presentation
      EPOCHAL TSUKUBA, Tsukuba-city, Japan (茨城県つくば市)
    • Year and Date
      2015-09-14
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Arnoldi-type contour integral-based eigensolver for solving nonlinear eigenvalue problems2015

    • Author(s)
      Akira Imakura, Tetsuya Sakurai
    • Organizer
      ICIAM 2015
    • Place of Presentation
      Beijing, China
    • Year and Date
      2015-08-10
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Shifted Block BiCGSTAB(l)法の構築とその近似解の精度について2015

    • Author(s)
      齋藤 周作, 多田野 寛人, 今倉 暁
    • Organizer
      第44回 数値解析シンポジウム (NAS2015)
    • Place of Presentation
      ぶどうの丘(山梨県甲州市)
    • Year and Date
      2015-06-08
    • Related Report
      2015 Annual Research Report
  • [Presentation] Inherent error resilience of a complex moment-based eigensolver for solving interior eigenvalue problem2015

    • Author(s)
      Akira Imakura, Yasunori Futamura, Tetsuya Sakurai
    • Organizer
      2015 LBNL - Tsukuba Joint Meeting
    • Place of Presentation
      LBNL, USA
    • Year and Date
      2015-05-28
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Fault tolerance inherent in a complex moment-based eigensolver2015

    • Author(s)
      Akira Imakura, Yasunori Futamura, Tetsuya Sakurai
    • Organizer
      Sparse Solvers for Exascale: From Building Blocks to Applications
    • Place of Presentation
      Greifswald (Germany)
    • Year and Date
      2015-03-23
    • Related Report
      2014 Research-status Report
  • [Presentation] Inherent Error Resilience of a Complex Moment-Based Eigensolver2015

    • Author(s)
      Akira Imakura, Yasunori Futamura, Tetsuya Sakurai
    • Organizer
      SIAM Conference on Computational Science and Engineering (CSE15)
    • Place of Presentation
      Salt Lake City (USA)
    • Year and Date
      2015-03-14
    • Related Report
      2014 Research-status Report
  • [Presentation] Error resilience strategy of a complex moment-based eigensolver2015

    • Author(s)
      Akira Imakura, Yasunori Futamura, Tetsuya Sakurai
    • Organizer
      Annual Meeting on Advanced Computing System and Infrastructure (ACSI) 2015
    • Place of Presentation
      筑波国際会議場(茨城)
    • Year and Date
      2015-01-26
    • Related Report
      2014 Research-status Report
  • [Presentation] 各種周回積分型固有値解法の関係性について2014

    • Author(s)
      今倉 暁, 杜 磊, 櫻井 鉄也
    • Organizer
      2014年度 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)
    • Year and Date
      2014-10-08
    • Related Report
      2014 Research-status Report
  • [Presentation] 実数計算のみを利用した周回積分型固有値解法における精度悪化とその対処2014

    • Author(s)
      長谷川 哲也, 今倉 暁, 櫻井 鉄也
    • Organizer
      第8回協定講座シンポジウム
    • Place of Presentation
      神戸大学(兵庫)
    • Year and Date
      2014-09-11
    • Related Report
      2014 Research-status Report
  • [Presentation] Communication-Avoiding Arnoldi版周回積分型固有値解法2014

    • Author(s)
      今倉 暁, 杜 磊, 櫻井 鉄也
    • Organizer
      日本応用数理学会 2014年度年会
    • Place of Presentation
      政策研究大学院大学(東京)
    • Year and Date
      2014-09-03
    • Related Report
      2014 Research-status Report
  • [Presentation] Block BiCGSTAB(l)法の計算量削減2014

    • Author(s)
      齋藤 周作, 多田野 寛人, 今倉 暁
    • Organizer
      日本応用数理学会 2014年度年会
    • Place of Presentation
      政策研究大学院大学(東京)
    • Year and Date
      2014-09-03
    • Related Report
      2014 Research-status Report
  • [Presentation] 周回積分型固有値解法の数理的耐故障性について2014

    • Author(s)
      今倉 暁, 櫻井 鉄也
    • Organizer
      2014年並列/分散/協調処理に関する『新潟』サマー・ワークショップ(SWoPP新潟2014)
    • Place of Presentation
      朱鷺メッセ 新潟コンベンションセンター(新潟)
    • Year and Date
      2014-07-28
    • Related Report
      2014 Research-status Report
  • [Presentation] A Novel Contour Integral Based Eigensolver for Solving Linear and Nonlinear Eigenvalue Problems2014

    • Author(s)
      Akira Imakura, Lei Du, Tetsuya Sakurai
    • Organizer
      East Asia Section of SIAM (EASIAM) 2014
    • Place of Presentation
      Ambassador City Jomtien (Thailand)
    • Year and Date
      2014-06-23
    • Related Report
      2014 Research-status Report
  • [Presentation] Two-Stage Simultaneous Band Reduction for Two Dense Symmetric Matrices2014

    • Author(s)
      Lei Du, Akira Imakura, Tetsuya Sakurai
    • Organizer
      East Asia Section of SIAM (EASIAM) 2014
    • Place of Presentation
      Ambassador City Jomtien (Thailand)
    • Year and Date
      2014-06-23
    • Related Report
      2014 Research-status Report
  • [Presentation] Hankel行列版周回積分型固有値解法の精度解析2014

    • Author(s)
      今倉 暁, 杜 磊, 長谷川 哲也, 櫻井 鉄也
    • Organizer
      第43回 数値解析シンポジウム -NAS2014-
    • Place of Presentation
      ホテル日航八重山(沖縄)
    • Year and Date
      2014-06-11
    • Related Report
      2014 Research-status Report
  • [Presentation] On error resilience of a complex moment-based eigensolver2014

    • Author(s)
      Tetsuya Sakurai, Yasunori Futamura, Akira Imakura
    • Organizer
      10th International Workshop on Accurate Solution of Eigenvalue Problems (IWASEP10)
    • Place of Presentation
      Dubrovnik (Croatia)
    • Year and Date
      2014-06-02
    • Related Report
      2014 Research-status Report
  • [Presentation] Accuracy analysis on the Rayleigh-Ritz type of the contour integral based eigensolver2014

    • Author(s)
      Akira IMAKURA, Lei DU, Tetsuya SAKURAI
    • Organizer
      International Workshop on Eigenvalue Problems: Algorithms; Software and Applications, in Petascale Computing (EPASA2014)
    • Place of Presentation
      つくば国際会議場
    • Related Report
      2013 Research-status Report
  • [Presentation] A high accuracy Block Krylov subspace method based on the bi-conjugate residual approach2014

    • Author(s)
      Hiroto TADANO, Akira IMAKURA
    • Organizer
      International Workshop on Eigenvalue Problems: Algorithms; Software and Applications, in Petascale Computing (EPASA2014)
    • Place of Presentation
      つくば国際会議場
    • Related Report
      2013 Research-status Report
  • [Presentation] 疎行列向け直接法に基づく重み付き定常反復法2014

    • Author(s)
      今倉 暁, 櫻井 鉄也
    • Organizer
      新学術領域研究「コンピューティクスによる物質デザイン:複合相関と非平衡ダイナミクス」平成25年度 第2回研究会
    • Place of Presentation
      東京大学
    • Related Report
      2013 Research-status Report
  • [Presentation] 複数右辺ベクトルを持つ連立一次方程式に対する双共役残差型アプローチに基づく高精度Block Krylovアルゴリズムについて2014

    • Author(s)
      多田野 寛人, 今倉 暁
    • Organizer
      新学術領域研究「コンピューティクスによる物質デザイン:複合相関と非平衡ダイナミクス」平成25年度 第2回研究会
    • Place of Presentation
      東京大学
    • Related Report
      2013 Research-status Report
  • [Presentation] Rayleigh-Ritz法に基づく周回積分型固有値解法の精度解析2014

    • Author(s)
      今倉 暁, 杜 磊, 櫻井 鉄也
    • Organizer
      Kunitachi One-Day Symposium on Applied Mathematics and Related Topics
    • Place of Presentation
      一橋大学
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] 疎行列向け直接解法に基づく定常反復法および前処理としての有効性2014

    • Author(s)
      今倉 暁
    • Organizer
      環瀬戸内応用数理研究部会 第17回シンポジウム
    • Place of Presentation
      愛媛大学
    • Related Report
      2013 Research-status Report
  • [Presentation] A Novel Interpretation for the Contour Integral-Based Spectral Projection Methods for Solving Generalized Eigenvalues Problems2013

    • Author(s)
      Akira IMAKURA, Lei DU, Tetsuya SAKURAI
    • Organizer
      The 9th East Asia SIAM Conference - The 2nd Conference on Industrial and Applied Mathematics
    • Place of Presentation
      The Newton Hotel, Indonesia
    • Related Report
      2013 Research-status Report
  • [Presentation] 双共役残差型反復解法の複数右辺ベクトル対応版への拡張と性能評価2013

    • Author(s)
      多田野 寛人, 石川 陽一, 今倉 暁
    • Organizer
      日本応用数理学会2013年度年会
    • Place of Presentation
      アクロス福岡
    • Related Report
      2013 Research-status Report
  • [Presentation] 線形方程式の数値解法と科学技術計算への応用2013

    • Author(s)
      今倉 暁
    • Organizer
      2013年度 数値線形代数研究集会
    • Place of Presentation
      東京理科大学
    • Related Report
      2013 Research-status Report
    • Invited
  • [Remarks] 個人ホームページ

    • URL

      http://www.cs.tsukuba.ac.jp/~imakura/index.html

    • Related Report
      2014 Research-status Report
  • [Remarks] 個人ホームページ

    • URL

      http://www.cs.tsukuba.ac.jp/~imakura/

    • Related Report
      2013 Research-status Report

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Published: 2014-07-25   Modified: 2019-07-29  

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