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New GMRES algorithm for solving large scale inverse problems on a cloud computing

Research Project

Project/Area Number 23654040
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeMulti-year Fund
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionKeio University

Principal Investigator

NODERA Takashi  慶應義塾大学, 理工学部, 教授 (50156212)

Co-Investigator(Kenkyū-buntansha) TANI Atsushi  慶應義塾大学, 理工学部, 名誉教授 (90118969)
OHNO Yoshio  慶應義塾大学, 理工学部, 名誉教授 (20051865)
YAMAMOTO Yoshikazu  慶應義塾大学, 理工学部, 旧教授 (20051873)
TAMURA Youzou  慶應義塾大学, 理工学部, 教授 (50171905)
Project Period (FY) 2011 – 2013
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords非適切な問題 / 離散型悪条件問題 / 逆問題 / GMRES / Krylov部分空間 / Tikhonov正則化 / 制約条件 / augmentation / GMRES法 / Tikhonov正則化法 / 線形悪条件問題 / Tikhonov値 / 並列計算 / 非適切問題 / 正則化法 / Tikhonov
Research Abstract

GMRES regularization method is arguably the most popular solution for linear discrete ill-posed problems. We explores different regularization methods as a means of yielding stable solutions for linear discrete ill-posed problems.
The regularization with GMRES must be implemented in two stages, which are designed to generate an approximate solution of a linear system through the use of GMRES, and to determine the most appropriate solution by using a constraint. In the first stage, particular behaviors of GMRES and preconditioned GMRES for linear discrete ill-posed problems are identified. In the second stage, a simplified Tikhonov threshold as a constraint to determine the best approximate solution is explored. Numerical experiments have been tabulated to underline the effectiveness of our proposed method.

Report

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

    (60 results)

All 2014 2013 2012 2011 Other

All Journal Article (26 results) (of which Peer Reviewed: 23 results) Presentation (33 results) Book (1 results)

  • [Journal Article] Effect of the Wetting Layer on the Fingering Pattern in a Hele-Shaw Cell2014

    • Author(s)
      H. Tani and A. Tani
    • Journal Title

      J. Phys. Soc. Japan

      Volume: 83 Pages: 34401-34401

    • NAID

      40020017740

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] An Efficient Implementation of the Block Gram-Schmidt Method2013

    • Author(s)
      Y. Matsuo and T. Nodera
    • Journal Title

      The ANZIAM J

      Volume: Vol.54

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] An Inverse Problem for Pseudoparabolic Equation of Filtration : the Stabilization2013

    • Author(s)
      A. Sh. Lyubanova and A. Tani
    • Journal Title

      Appl. Anal

      Volume: Vol.92 Pages: 573-585

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Free boundary Problem of the One-dimensional Equations for Viscous and heatconductive Gaseous Flow under the Self-gravitation2013

    • Author(s)
      M. Umehara and A. Tani
    • Journal Title

      Math. Models Mech. Appl. Sci

      Volume: Vol.23 Pages: 1377-1419

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] An Efficient Implementation of the Block Gram-Schmidt Method2013

    • Author(s)
      Yoichi Matsuo, Takashi Nodera
    • Journal Title

      ANZIAM J.

      Volume: 54(E)

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] An Inverse Problem for Pseudoparabolic Equation of Filtration: the Stabilization2013

    • Author(s)
      A. Sh. Lyubanova and A. Tani
    • Journal Title

      Appl. Anal.

      Volume: 92 Pages: 573-585

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Free-boundary Problem of the One-dimensional Equations for Viscous and Heat-conductive Gaseous Flow under the Self-gravitation2013

    • Author(s)
      M. Umehara and A. Tani
    • Journal Title

      Math. Models Meth. Appl. Sci.

      Volume: 23 Pages: 1377-1419

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] An efficient implementation of the block Gram-Schmidt method2013

    • Author(s)
      Youichi Matsuo, Takashi Nodera
    • Journal Title

      ANZIAM Journal

      Volume: 55(E)

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Two-level Parallel Preconditioning derived from an approximate inverse based on the Sharman-Morrison formula2012

    • Author(s)
      L. Zhang, K. Moriya, and T. Nodera
    • Journal Title

      The ANZIAM J

      Volume: Vol.54(E)

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] New Stopping Rule : GMRES for Linear Discrete Illposed Problems2012

    • Author(s)
      N. Kuroiwa and T. Nodera
    • Journal Title

      Keio Math. Sem. Report

      Pages: 2-1

    • Related Report
      2013 Final Research Report
  • [Journal Article] Parallel Gram- Schmidt Orthogonalization with Optimal Block-size2012

    • Author(s)
      Y. Matsuo and T. Nodera
    • Journal Title

      VECPAR2012, Proceedings

      Pages: 51-52

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Limiting Behavior of Multidimensional Diffusion Process in Levy Environments with Different Indices2012

    • Author(s)
      田村 要三
    • Journal Title

      統計数理研究所共同研究レポート

      Volume: Vol.275 Pages: 129-135

    • Related Report
      2013 Final Research Report
  • [Journal Article] Global Solution to the Conserved Phase-field Equation of Penrose --Fife type2012

    • Author(s)
      A. Tani
    • Journal Title

      Comm. Appl. Anal

      Volume: 16 Pages: 703-726

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Two-level pallel pconditioning drived from an aroximate Ierse based on the Sharman-Morrison Formula2012

    • Author(s)
      Zhang Linjie, Kentaro Moriya, Takashi Nodera
    • Journal Title

      ANZIAM Journal

      Volume: 54(E)

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Small-time existence of a strong solution of primitive equations for the ocean2012

    • Author(s)
      H. Honda, Atsusi Tani
    • Journal Title

      Tokyo Journal Mathematics

      Volume: 35 Pages: 97-138

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Asymptotic behaviour at a tip of a rigid line inclusion in linearized elasticity2012

    • Author(s)
      H. Itou, A. M. Khludnev, E. M. Rudoy, Atsusi Tani
    • Journal Title

      Zeitschr. Angew. Math. Mech.

      Volume: 92 Pages: 716-730

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Global solution to the conserved phase-field equation of Penrose-Fife type2012

    • Author(s)
      Atsusi Tani
    • Journal Title

      Comm. Appl. Anal.

      Volume: 16 Pages: 703-726

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] 離散型線形悪条件問題に対する修正GMRES法2011

    • Author(s)
      黒岩 奈保, 野寺 隆
    • Journal Title

      情報処理学会論文誌

      Volume: Vol.52 Pages: 2812-2821

    • NAID

      110008608842

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] A GMRES(m) Method with Two Stage Deflated Preconditioners2011

    • Author(s)
      J. Shiroishi and T. Nodera
    • Journal Title

      The ANZIAM J

      Volume: Vol.52

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] The Optimal Block Size for the Block Gram-Schmidt Orthogonalization2011

    • Author(s)
      Y. Matsuo and T. Nodera
    • Journal Title

      J. of Science and Technology

      Volume: Vol.49 Pages: 348-354

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the Hasegawa-Wakatani Equations with Vanishing Resistivity2011

    • Author(s)
      S. Kondo and A. Tani
    • Journal Title

      Proc. Japan Acad. Ser. A Math. Sci

      Volume: Vol.9 Pages: 156-166

    • NAID

      40019128058

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] SPHベースリアルタイム火炎シミュレーション2011

    • Author(s)
      間淵 聡, 藤代 一成, 大野 義夫
    • Journal Title

      情報処理学会論文誌

      Volume: Vol.52 Pages: 2965-2972

    • NAID

      110008665642

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] The Optimal Block-size for the Block Gram-Schmidt Orthogonalization2011

    • Author(s)
      Youichi. Matsuo, Takashi. Nodera
    • Journal Title

      Journal of Science and Technology

      Volume: 49 Pages: 348-354

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] 離散型線形悪条件問題に対する修正GMRES法2011

    • Author(s)
      黒岩 奈保, 野寺 隆
    • Journal Title

      情報処理学会論文誌

      Volume: 52 Pages: 2812-2821

    • NAID

      110008608842

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] A GMRES(m) Method with Two Stage Deflated Preconditioners2011

    • Author(s)
      Jungo Shiroishi, Talashi Nodera
    • Journal Title

      ANZIAM J.

      Volume: 52

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] 最小二乗問題に対するblock Gram-Schmidt法の適用2011

    • Author(s)
      松尾洋一,野寺 隆
    • Journal Title

      研究報告ハイパフォーマンスコンピューティング

      Volume: 2011-HPC-130 Pages: 1-4

    • NAID

      110008583403

    • Related Report
      2011 Research-status Report
  • [Presentation] 非対称行列系に対する柔軟なILU 分解前処理について2014

    • Author(s)
      中村 貴稔, 野寺 隆
    • Organizer
      日本応用数理学会研究部会連合発表会『行列・固有値問題の解法とその応用』
    • Place of Presentation
      京都大学
    • Year and Date
      2014-03-20
    • Related Report
      2013 Final Research Report
  • [Presentation] Deflated GMRES 法の効率のよい近似逆前処理2014

    • Author(s)
      沓掛 拓朗, 野寺 隆
    • Organizer
      第76回情報処理学会全国大会
    • Place of Presentation
      東京電気大学
    • Related Report
      2013 Final Research Report
  • [Presentation] Effective Approximate Inverse Preconditioner for deflated FGMRES"2014

    • Author(s)
      T. Kutsukae and T. Nodera
    • Organizer
      2014 ACCEE
    • Place of Presentation
      Phuket, Thailand
    • Related Report
      2013 Final Research Report
  • [Presentation] A Note on Lanczos Algorithm for Computing PageRank2014

    • Author(s)
      K. Teramoto and T. Nodera
    • Organizer
      3rd Annual International Conference on Computer Mathematics, Computational Geometry & Statistics (CMCGS 2014)
    • Place of Presentation
      Singapore
    • Related Report
      2013 Final Research Report
  • [Presentation] A Note on Lanczos Algorithm for Computing PageRank2014

    • Author(s)
      Kazuma Teramoto, Takashi Nodera
    • Organizer
      3rd Annual International Conference on Computer Mathematics
    • Place of Presentation
      Singapore
    • Related Report
      2013 Annual Research Report
  • [Presentation] Flexible Deflated GMRES with AISM Precondtioner2014

    • Author(s)
      Takuro Kutsukake, Takashi Nodera
    • Organizer
      EPSA2014
    • Place of Presentation
      Tsukuba、Japan
    • Related Report
      2013 Annual Research Report
  • [Presentation] A Note on Flexible Incomplte LU Factorization2014

    • Author(s)
      Takatoshi Nakamura, Takashi Nodera
    • Organizer
      EPSA2014
    • Place of Presentation
      Tsukuba, Japan
    • Related Report
      2013 Annual Research Report
  • [Presentation] Effective Approximate Inverse Preconditioner for deflated FGMRES2014

    • Author(s)
      Takuro Kutsukake, Takashi Nodera
    • Organizer
      2014 ACCEE
    • Place of Presentation
      Phuket, Tailand
    • Related Report
      2013 Annual Research Report
  • [Presentation] Efficiency of Flexible ILU Preconditioner2014

    • Author(s)
      Takatoshi Nakamura, Takashi Nodera
    • Organizer
      2014 ACCEE
    • Place of Presentation
      Phuket, Tailand
    • Related Report
      2013 Annual Research Report
  • [Presentation] 柔軟な不完全LU分解前処理の有効性について2014

    • Author(s)
      中村貴稔,野寺 隆
    • Organizer
      第76回情報処理学会全国大会
    • Place of Presentation
      東京電機大学
    • Related Report
      2013 Annual Research Report
  • [Presentation] Deflated GMRES法の効率のよい近似逆前処理2014

    • Author(s)
      沓掛拓郎,野寺 隆
    • Organizer
      第76回情報処理学会全国大会
    • Place of Presentation
      東京電機大学
    • Related Report
      2013 Annual Research Report
  • [Presentation] 非対称行列系に対する柔軟なILU分解前処理について2014

    • Author(s)
      中村貴稔,野寺 隆
    • 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 Annual Research Report
  • [Presentation] Flexible Deflated GMRES 法の収束性の改善について2013

    • Author(s)
      沓掛 拓朗, 野寺 隆
    • Organizer
      情報処理学会第75回全国大会
    • Place of Presentation
      東北大学
    • Related Report
      2013 Final Research Report
  • [Presentation] Flexible なILU 分解のGMRES 法への応用2013

    • Author(s)
      中村 貴稔, 野寺 隆
    • Organizer
      情報処理学会第75回全国大会
    • Place of Presentation
      東北大学
    • Related Report
      2013 Final Research Report
  • [Presentation] Two phase free boundary problem of Magnetohydrodynamics2013

    • Author(s)
      A. Tani
    • Organizer
      Workshop on Boundary Phenomena for Evolutionary Partial Differential Equations
    • Place of Presentation
      Institute of Mathematics, Academia Sinica, Taipei, ROC
    • Related Report
      2013 Final Research Report
  • [Presentation] Glass transition : introductory survey2013

    • Author(s)
      谷 温之
    • Organizer
      現象解析特別セミナー第3回
    • Place of Presentation
      群馬大学
    • Related Report
      2013 Final Research Report
  • [Presentation] Astrophysical hydrodynamics I,II2013

    • Author(s)
      谷 温之
    • Organizer
      現象解析特別セミナー第4回
    • Place of Presentation
      東京理科大学
    • Related Report
      2013 Final Research Report
  • [Presentation] Two Phase Free Boundary Problem of Magnetohydrodynamics.2013

    • Author(s)
      A. Tani
    • Organizer
      Workshop on “Boundary Phenomena for Evolutionary Partial Differential Equations"
    • Place of Presentation
      Institute of Mathematics, Academia Sinica, Taipei, ROC
    • Related Report
      2013 Annual Research Report
  • [Presentation] Free Boundary Problems of Magnetohydrodynamics for Viscous Compressible Electrically Conducting Fluids2013

    • Author(s)
      A Tani
    • Organizer
      Mathematical Hydrodynamics and Parabolic Equations in honour of Vsevolod Solonnikov on the occasion of his 80th birthday
    • Place of Presentation
      Steklov Institute of Mathematics, St. Petersburg, Russia
    • Related Report
      2013 Annual Research Report
  • [Presentation] FlexibleなILU分解のGMRES法への応2013

    • Author(s)
      中村 貴稔,野寺 隆
    • Organizer
      情報処理学会第75回全国大会
    • Place of Presentation
      東北大学,仙台
    • Related Report
      2012 Research-status Report
  • [Presentation] Flexible Deflated GMRES法の収束性の改善について2013

    • Author(s)
      沓掛 拓朗,野寺 隆
    • Organizer
      情報処理学会第75回全国大会
    • Place of Presentation
      東北大学,仙台
    • Related Report
      2012 Research-status Report
  • [Presentation] 適切なblock-sizeの決定法を用いたBlock Gram-Schmidt 法の並列化2012

    • Author(s)
      松尾 洋一, 野寺 隆
    • Place of Presentation
      電気通信大学
    • Year and Date
      2012-06-01
    • Related Report
      2013 Final Research Report
  • [Presentation] An Efficient Implementation of the Block Gram-Schmidt Method2012

    • Author(s)
      Y. Matsuo and T. Nodera
    • Organizer
      CTAC 2012 in Brisbane
    • Place of Presentation
      Australia
    • Related Report
      2013 Final Research Report
  • [Presentation] 複素行列に対するRL-GMRES 法の有効性について2012

    • Author(s)
      上中 貴統, 野寺 隆
    • Organizer
      情報処理学会第74回全国大会
    • Place of Presentation
      名古屋工業大学
    • Related Report
      2013 Final Research Report
  • [Presentation] 適切なblock-sizeの決定法を用いたBlock Gram-Schmidt法の並列化2012

    • Author(s)
      松尾洋一, 野寺 隆
    • Organizer
      情報処理学会HPC研究会
    • Place of Presentation
      電気通信大学,東京
    • Related Report
      2012 Research-status Report
  • [Presentation] A Parallel Block Gram-Schmidt Orthogonalization with an Optimal Block-siz2012

    • Author(s)
      Youichi Matsuo, Takashi Nodera
    • Organizer
      VECPAR 2012
    • Place of Presentation
      Kobe, Japan
    • Related Report
      2012 Research-status Report
  • [Presentation] An Efficient Implementation of the Block Gram-Schmidt Method2012

    • Author(s)
      Youichi Matsuo, Takashi Nodera
    • Organizer
      CTAC 2012
    • Place of Presentation
      Brisbane, Australia
    • Related Report
      2012 Research-status Report
  • [Presentation] マルチパラメータによる修正不完全コレスキー分解の高速化2012

    • Author(s)
      中村貴稔,野寺 隆
    • Organizer
      情報処理学会第74回全国大会
    • Place of Presentation
      名古屋工業大学
    • Related Report
      2011 Research-status Report
  • [Presentation] Constructing Approximate Solutions in Regularization Methods for Linear Discrete Ill-Posed Problems2011

    • Author(s)
      N. Kuroiwa and T. Nodera
    • Organizer
      Science MATLAB workshop 2011
    • Place of Presentation
      Keio University
    • Year and Date
      2011-10-19
    • Related Report
      2013 Final Research Report
  • [Presentation] The Optimal Block-size for the Block Gram-Schmidt Orthogonalization2011

    • Author(s)
      Youichi. Matsuo, Takashi. Nodera
    • Organizer
      ACOMP 2011
    • Place of Presentation
      Ho Chi Minh City, Vietnam
    • Related Report
      2011 Research-status Report
  • [Presentation] Constructing Approximate Solutions in Regularization Methods for Linear Discrete Ill-Posed Problems2011

    • Author(s)
      Nao Kuroiwa, Takashi Nodera
    • Organizer
      Science MATLAB Workshop2011(招待講演)
    • Place of Presentation
      慶應義塾大学理工学部
    • Related Report
      2011 Research-status Report
  • [Presentation] RL-GMRES法の実装と有効性について

    • Author(s)
      上中 貴統,野寺 隆
    • Organizer
      日本応用数理学会2011年会
    • Place of Presentation
      同志社大学
    • Related Report
      2011 Research-status Report
  • [Presentation] Flexible GMRES法の収束改善につい

    • Author(s)
      沓掛 拓郎,野寺 隆
    • Organizer
      情報処理学会第74回全国大会
    • Place of Presentation
      名古屋工業大学
    • Related Report
      2011 Research-status Report
  • [Book] 「数式処理と計算ツール」, 『情報学基礎』, 慶應義塾大学理工学部編2013

    • Author(s)
      野寺 隆
    • Publisher
      共立出版
    • Related Report
      2013 Final Research Report

URL: 

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

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