General research which aims at the hybrid iteration method for a matrix equation including a non-diagonal dominant matrix

• Project/Area Number: 21540156
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Okayama University of Science
• Principal Investigator: NIKI Hiroshi 岡山理科大学, 名誉教授 (30068879)
• Co-Investigator(Kenkyū-buntansha): HARUKI Shigeru 岡山理科大学, 理学部, 教授 (60140480) ; HAMAYA Yoshihiro 岡山理科大学, 総合情報学部, 教授 (40228549) ; KOHNO Toshiyuki 岡山理科大学, 総合情報学部, 准教授 (90309534) ; NIKI Masato 東海大学, 海洋学部, 准教授 (30408033)
• Project Period (FY): 2009 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000); Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: 前処理法 / 定常反復法 / クリロフ部分空間法 / 行列方程式 / 反復法 / 前処理 / ハイブリット法 / Krylov部分空間法

Research Abstract

We have proposed new effective preconditioner for the regular iterative method and proved the comparison theorem of its method. The preconditioned matrix uses some elements of the coefficient matrix, and we studied the effective technique of having combined two pretreatments. Furthermore, we proposed the SOR-like method as a preconditioner of the krylov subspace method. We showed the numerical results of SOR-like-CGS and SOR-like-BiCGStab.

Research Products

• [Journal Article] Existence of pseudo almost periodic solutions of linear Volterra integrodifferential equations (2011)
  • Author(s): Y.Hamanaka, Y.Hamaya
  • Journal Title: Analele Stiintifice ale Universitatii 'Al.I.Cuza' Mathematica, Tomul Volume: LVII Pages: 87-102
  • Peer Reviewed
• [Journal Article] Stability properties and almost periodic solutions of abstract functional differential equations with infinite delay (2011)
  • Author(s): Y.Hamaya
  • Journal Title: Libertys Mathematica Volume: XXXI Pages: 93-102
  • Peer Reviewed
• [Journal Article] Gauss-Seidel反復法に対する前処理の組み合わせによる影響について (2010)
  • Author(s): 河野敏行, 新田敏弘, 仁木滉
  • Journal Title: 日本応用数理学会論文誌 Volume: Vol.20, No.2 Pages: 131-145
  • NAID: 110007658201
  • Peer Reviewed
• [Journal Article] On the preconditioned SOR-like algorithm (2010)
  • Author(s): Toshiyuki Kohno, Toshihiro Nitta, Hiroshi Niki
  • Journal Title: INFORMATION Volume: Vol.13, No.3 Pages: 871-876
  • Peer Reviewed
• [Journal Article] On the GS iterative method with I+S type preconditioner (2010)
  • Author(s): Toshihiro Nitta, Toshiyuki Kohno, and Hiroshi Niki
  • Journal Title: INFORMATION Volume: Vol.13, No.3 Pages: 857-861
  • Peer Reviewed
• [Journal Article] On the GS iterative method with I+S type preconditioner (2010)
  • Author(s): Toshihiro Nitta, Toshiyuki Kohno, Hiroshi Niki
  • Journal Title: INFORMATION Volume: 13,3(B) Pages: 857-861
  • Peer Reviewed
• [Journal Article] A note on the preconditioner Pm=(I+Sm) (2009)
  • Author(s): Toshiyuki Kohno and Hiroshi Niki
  • Journal Title: Journal of Computational and Applied Mathematics Volume: Vol.225, No.1 Pages: 316-319
  • Peer Reviewed
• [Journal Article] An extended GS method for dense linear system (2009)
  • Author(s): Hiroshi Niki, Toshiyuki Kohno and Kuniyoshi Abe
  • Journal Title: Journal of Computational and Applied Mathematics Volume: Vol.231, No.1 Pages: 177-186
  • Peer Reviewed
• [Journal Article] A classification of H-m atrix (2009)
  • Author(s): Masataka Usui, Hiroshi Niki and Toshiyuki Kohno
  • Journal Title: International Journal of Nume rical Methods and Applications Volume: Vol.1, No.1 Pages: 53-62
  • Peer Reviewed
• [Journal Article] A note on the preconditioner Pm=(I+Sm) (2009)
  • Author(s): Toshiyuki Kohno, Hiroshi Niki
  • Journal Title: Journal of Computational and Applied Mathematics 225, 1 Pages: 316-319
  • Peer Reviewed
• [Journal Article] An extended GS method for dense linear system (2009)
  • Author(s): Hiroshi Niki, Toshiyuki Kohno, Kuniyoshi Abe
  • Journal Title: Journal of Computational and Applied Mathematics 231, 1 Pages: 177-186
  • Peer Reviewed
• [Journal Article] A classification of H-matrix (2009)
  • Author(s): Masataka Usui, Hiroshi Niki, Toshiyuki Kohno
  • Journal Title: International Journal of Numerical Methods and Applications 1, 1 Pages: 53-62
  • Peer Reviewed
• [Presentation] 前処理付定常反復アルゴリズムの比較 (2011)
  • Author(s): 河野敏行, 新田敏弘, 仁木滉
  • Organizer: 日本応用数理学会環瀬戸内応用数理研究部会
  • Place of Presentation: 山口東京理科大学(山口)
  • Year and Date: 2011-12-03
• [Presentation] On the SOR-like preconditioner (2011)
  • Author(s): Toshiyuki Kohno
  • Organizer: Int. Workshop on application of iterative methods to engineering and its mathematical element
  • Place of Presentation: 同志社大学(京都)
  • Year and Date: 2011-10-23
• [Presentation] The PSOR-like preconditioner for CGS method (2011)
  • Author(s): Toshihiro Nitta, Toshiyuki Kohno and Hiroshi Niki
  • Organizer: Precond2011(International Conference On Preconditioning Techniques For Scientific And Industrial Applications)
  • Place of Presentation: ボルドー第1大学(フランス)
  • Year and Date: 2011-05-18
• [Presentation] The PSOR-like preconditioner for CGS method (2011)
  • Author(s): Toshihiro Nitta, Toshiyuki Kohno, Hiroshi Niki
  • Organizer: Precond2011 (International Conference On Preconditioning Techniques For Scientific And Industrial Applications)
  • Place of Presentation: ボルドー第1大学(フランス)
  • Year and Date: 2011-05-18
• [Presentation] On the SOR-like method as preconsitioner of CGS (2010)
  • Author(s): Toshiyuki Kohno, Toshihiro Nitta and Hiroshi Niki
  • Organizer: International congress on Computational and Applied Mathematics
  • Place of Presentation: ルーバンカトリック大学(ペルギー)
  • Year and Date: 2010-07-06
• [Presentation] On the SOR-like method as preconsitioner of CGS (2010)
  • Author(s): Toshiyuki Kohno, Toshihiro Nitta, Hiroshi Niki
  • Organizer: International congress on Computational and Applied Mathematics
  • Place of Presentation: ベルギー
  • Year and Date: 2010-07-06
• [Presentation] On the preconditioned SOR-like algorithm (2009)
  • Author(s): Toshiyuki Kohno, Toshihiro Nitta and Hiroshi Niki
  • Organizer: The Fifth International Conference on Information
  • Place of Presentation: 京都大学(京都)
• [Presentation] On the preconditioned SOR-like algorithm (2009)
  • Author(s): Toshiyuki Kohno, Toshihiro Nitta, Hiroshi Niki
  • Organizer: The Fifth International Conference on Information
  • Place of Presentation: 京都大学
• [Presentation] On the GS iterative method with I+S type preconditioner (2009)
  • Author(s): Toshihiro Nitta, Toshiyuki Kohno, Hiroshi Niki
  • Organizer: The Fifth International Conference on Information
  • Place of Presentation: 京都大学
• [Presentation] 前処理付定常反復アルゴリズムについて (2009)
  • Author(s): 河野敏行, 新田敏弘, 仁木滉
  • Organizer: 日本応用数理学会2009年度年会
  • Place of Presentation: 大阪大学
• [Presentation] 前処理付定常反復アルゴリズムを利用した計算結果について (2009)
  • Author(s): 新田敏弘, 河野敏行, 仁木滉
  • Organizer: 環瀬戸内応用数理研究部会2009年度年会
  • Place of Presentation: 徳島大学
• [Presentation] 前処理付SOR-likeアルゴリズムの数値結果について (2009)
  • Author(s): 河野敏行, 新田敏弘, 仁木滉
  • Organizer: 環瀬戸内応用数理研究部会2009年度年会
  • Place of Presentation: 徳島大学