Fast enclosure for solutions in eigenvalue problems

• Project/Area Number: 19760055
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Engineering fundamentals
• Research Institution: Gifu University
• Principal Investigator: MIYAJIMA Shinya Gifu University, 工学部, 准教授 (20367072)
• Project Period (FY): 2007 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥3,860,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥660,000); Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2007: ¥1,000,000 (Direct Cost: ¥1,000,000)
• Keywords: 数理工学(数理的解析・計画・設計) / 固有値問題 / 解の存在証明 / 精度保証

Research Abstract

We developed theory and algorithms for numerically enclosing solutions in eigenvalue problems.

Research Products

• [Journal Article] Fast enclosure for solutions in underdetermined systems (2010)
  • Author(s): Shinya Miyajima
  • Journal Title: Journal of Computational and Applied Mathematics Vol.234, Issue 12 Pages: 3436-3444
• [Journal Article] Fast verification for all eigenpairs in symmetric positive definite generalized eigenvalue problems (2010)
  • Author(s): S.Miyajima, T.Ogita, S.M.Rump, S.Oishi
  • Journal Title: Reliable Computing Vol.14 Pages: 24-45
• [Journal Article] Fast enclosure for all eigenvalues in generalized eigenvalue problems (2010)
  • Author(s): Shinya Miyajima
  • Journal Title: Journal of Computational and Applied Mathematics Vol.233, Issue 11 Pages: 2994-3004
• [Journal Article] Fast enclosure for solutions in underdetermined systems (2010)
  • Author(s): Shinya Miyajima
  • Journal Title: J.Computational and Applied Mathematics Volume: 234 Pages: 3436-3444
  • Peer Reviewed
• [Journal Article] Fast verification for all eigenpairs in symmetric positive definite generalized eigenvalue problems (2010)
  • Author(s): S.Miyajima, T.Ogita, S.M.Rump, S.Oishi
  • Journal Title: Reliable Computing Volume: 14 Pages: 24-45
  • Peer Reviewed
• [Journal Article] Fast enclosure for all eigenvalues in generalized eigenvalue problems (2010)
  • Author(s): Shinya Miyajima
  • Journal Title: J.Computational and Applied Mathematics Volume: 233 Pages: 2994-3004
  • Peer Reviewed
• [Journal Article] Fast Enclosure for All Eigenvalues in Generalized Eigenvalue Problems (2010)
  • Author(s): Shinya Miyajima
  • Journal Title: Journal of Computational and Applied Mathematics 233(11) Pages: 2994-3004
  • Peer Reviewed
• [Journal Article] Fast Verification for All Eigenpairs in Symmetric Positive Definite Generalized Eigenvalue Problems (2009)
  • Author(s): Shinya Miyajima
  • Journal Title: Reliable Computing (印刷中)
  • Peer Reviewed
• [Journal Article] Fast Verification for All Eigenpairs in Symmetric Positive Definite Generalized Eigenvalue Problems (2008)
  • Author(s): Shinya Miyajima, Takeshi Ogita, Siegfried M. Rump, Shin'ichi Oishi
  • Journal Title: Reliable Computing
  • Peer Reviewed
• [Presentation] Error bounds for computed eigenvalues in generalized eigenvalue problem (2010)
  • Author(s): Shinya Miyajima
  • Organizer: 14th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics
  • Place of Presentation: Ecole Normale Superieurede Lyon
  • Year and Date: 2010-09-28
• [Presentation] Enclosing all eigenpairs in symmetric positive definite generalized eigenvalue problems (2010)
  • Author(s): Shinya Miyajima
  • Organizer: The 8th International Conference of Numerical Analysis and Applied Mathematics
  • Place of Presentation: Rodos Palace
  • Year and Date: 2010-09-20
• [Presentation] 一般化固有値問題における各固有値に対する数値的包含 (2010)
  • Author(s): 宮島信也
  • Organizer: 日本応用数理学会2010年度年会
  • Place of Presentation: 明治大学
  • Year and Date: 2010-09-06
• [Presentation] Numerical Inclusion for All Eigenvalues in Generalized Eigenvalue Problems (2010)
  • Author(s): 宮島信也
  • Organizer: デジタル解析学セミナー
  • Place of Presentation: 早稲田大学
  • Year and Date: 2010-01-27
• [Presentation] Numerical Inclusion for All Eigenvalues in Generalized Eigenvalue Problemes (2010)
  • Author(s): 宮島信也
  • Organizer: デジタル解析学セミナー
  • Place of Presentation: 早稲田大学
  • Year and Date: 2010-01-27
• [Presentation] Error bounds for computed eigenvalues in generalized eigenvalue problem, Proc.14th GAMM-IMACS International Symposium on Scientific Computing (2010)
  • Author(s): Shinya Miyajima
  • Organizer: Computer Arithmetic and Validated Numerics
  • Place of Presentation: 95-96(Lyon, France)
• [Presentation] Enclosing all eigenpairs in symmetric positive definite generalized eigenvalue problems, Proc.The 8th International Conference of Numerical Analysis and Applied Mathematics (2010)
  • Author(s): Shinya Miyajima
  • Organizer: Island of Rhodes
  • Place of Presentation: 945-948(Greece)
• [Presentation] 一般化固有値問題における各固有値に対する数値的包含 (2010)
  • Author(s): 宮島信也
  • Organizer: 日本応用数理学会2010年度年会講演予稿集
  • Place of Presentation: 49-50(明治大学)
• [Presentation] 一般化固有値問題におけるすべての固有値の数値的包含 (2009)
  • Author(s): 宮島信也
  • Organizer: 日本応用数理学会2009年度年会
  • Place of Presentation: 大阪大学
  • Year and Date: 2009-09-30
• [Presentation] 一般化固有値問題におけるすべての固有値の数値的包含 (2009)
  • Author(s): 宮島信也
  • Organizer: 日本応用数理学会2009年度年会講演予稿集
  • Place of Presentation: 305-306(大阪大学)
• [Presentation] Enclosing All Eigenvalues in Generalized Eigenvalue Problem (2008)
  • Author(s): Shinya Miyajima
  • Organizer: 13th GAMM IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics
  • Place of Presentation: The University of Texas at El Paso
  • Year and Date: 2008-09-29
• [Presentation] Enclosing All Eigenvalues in Generalized Eigenvalue Problem (2008)
  • Author(s): Shinya Miyajima
  • Organizer: 3th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics
  • Place of Presentation: The University of Texas at EI Paso(米国)
  • Year and Date: 2008-09-29
• [Presentation] Verifying All Eigenvalues in Generalized Eigenvalue Problem (2008)
  • Author(s): Shinya Miyajima, Michael Plum, Takeshi Ogita, Shin'ichi Oishi
  • Organizer: 2008 International Workshop on Numerical Verification and its Applications
  • Place of Presentation: Tokyo Dai-ichi Hotel
  • Year and Date: 2008-03-05
• [Presentation] Enclosing all eigenvalues in generalized eigenvalue problem, Proc.13th GAMM-IMACS International Symposium on Scientific Computing (2008)
  • Author(s): Shinya Miyajima
  • Organizer: Computer Arithmetic and Validated Numerics
  • Place of Presentation: 73-74(Texas, US)
• [Presentation] 実対称正定値一般化固有値問題における解の高速精度保証 (2007)
  • Author(s): 宮島信也
  • Organizer: 岐阜非線形セミナー
  • Place of Presentation: 岐阜大学
  • Year and Date: 2007-12-21
• [Presentation] 一般化固有値問題における解の高速精度保証 (2007)
  • Author(s): 宮島信也
  • Organizer: 第1回数理デザイン研究コロキウム
  • Place of Presentation: 岐阜大学
  • Year and Date: 2007-10-24
• [Presentation] Verified All Eigenpairs of Generalized Eigenvalue Problem (2007)
  • Author(s): Shinya Miyajima, Takeshi Ogita, Siegfried M. Rump, Shin'ichi Oishi
  • Organizer: 精度保証付き数値計算とその周辺」ワークショップ
  • Place of Presentation: 岐阜大学
  • Year and Date: 2007-10-12
• [Presentation] 一般化固有値問題におけるすべての固有対の高速精度保証 (2007)
  • Author(s): 宮島信也, 荻田武史, Siegfried M. Rump, 大石進一
  • Organizer: 日本応用数理学会2007年度年会
  • Place of Presentation: 北海道大学
  • Year and Date: 2007-09-16
• [Presentation] Verifying All Eigenpairs in Real Symmetric Positive Definite Generalized Eigenvalue Problem (2007)
  • Author(s): Shinya Miyajima, Takeshi Ogita, Shin'ichi Oishi
  • Organizer: 6th International Congress on Industrial and Applied Mathematics
  • Place of Presentation: ETH Zurich
  • Year and Date: 2007-07-16
• [Presentation] Verifying All Eigenpairs in Real Symmetric Positive Definite Generalized Eigenvalue Problem (2007)
  • Author(s): Shinya Miyajima
  • Organizer: 6th International Congress on Industrial and Applied Mathematics
  • Place of Presentation: Universitat Zurich
  • Year and Date: 2007-07-16
• [Presentation] 実対称正定値一般化固有値問題におけるすべての固有対の精度保証 (2007)
  • Author(s): 宮島信也, 荻田武史, Siegfried M. Rump, 大石進一
  • Organizer: 第36回数値解析シンポジウム
  • Place of Presentation: ウェルシティ湯河原
  • Year and Date: 2007-06-21
• [Presentation] Verified All Eigenpairs of Generalized Eigenvalue Problem (2007)
  • Author(s): Shinya Miyajima, Takeshi Ogita, Siegfried M. Rump, Shin'ichi Oishi
  • Organizer: International Workshop on Numerical Verification and its Applications
  • Place of Presentation: Waseda University
  • Year and Date: 2007-03-01
• [Presentation] Verifying all eigenpairs in real symmetric positive definite generalized eigenvalue problem (2007)
  • Author(s): S.Miyajima, T.Ogita, S.Oishi
  • Organizer: Proc.6th International Congress on Industrial and Applied Mathematics
  • Place of Presentation: 2020061-2020062(Zurich, Switzerland)
• [Presentation] 一般化固有値問題におけるすべての固有対の高速精度保証 (2007)
  • Author(s): 宮島信也, 荻田武史, Siegfried M.Rump, 大石進一
  • Organizer: 日本応用数理学会2007年度年会講演予稿集
  • Place of Presentation: 220-221(北海道大学)
• [Presentation] 実対称正定値一般化固有値問題におけるすべての固有対の精度保証 (2007)
  • Author(s): 宮島信也, 荻田武史, Siegfried M.Rump, 大石進一
  • Organizer: 第36回数値解析シンポジウム講演予稿集
  • Place of Presentation: 137-140(ウェルシティ湯河原)