Research on fast numerical methods for large-scale eigenvalue problems

• Project/Area Number: 24760061
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Engineering fundamentals
• Research Institution: Fukuoka Institute of Technology (2015); Nagoya University (2012-2014)
• Principal Investigator: MIYATA TAKAFUMI 福岡工業大学, 情報工学部, 准教授 (90581645)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000); Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2012: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
• Keywords: 固有値問題 / 高速高精度アルゴリズム / Jacobi-Davidson法 / 計算科学 / 数理工学 / ビッグデータ解析 / 高速解法 / 固有値問題の数値解法

Outline of Final Research Achievements

This research aims to develop fast and accurate numerical methods to solve eigenvalue problems. The results obtained in this research are as follows: (1) A framework to derive iterative methods (2) Rederivations of the existing Jacobi-Davidson method and its variants using the framework (3) New methods to improve the issues clarified in the rederivations (4) Fast and accurate algorithms for practical needs in eigenvalue computations.

Research Products

• [Journal Article] Computing surface Green's functions for semi-infinite systems on multilayered periodic structures (2016)
  • Author(s): T. Miyata, R. Naito, S. Honda
  • Journal Title: Journal of Engineering Mathematics Volume: 97 Issue: 1 Pages: 25-32
  • DOI: 10.1007/s10665-015-9794-x
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Clinicopathologic analysis of 6 lymphomatoid gastropathy cases: expanding the disease spectrum to CD4-CD8+ cases. (2015)
  • Author(s): Takata K, Noujima-Harada M, Miyata-Takata T, Ichimura K, Sato Y, Miyata T, Naruse K, Iwamoto T, Tari A, Masunari T, Sonobe H, Okada H, Iwamuro M, Mizobuchi K, Gion Y, Yoshino T.
  • Journal Title: Am J Surg Pathol. Volume: 39 Issue: 9 Pages: 1259-66
  • DOI: 10.1097/pas.0000000000000443
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Elevation of serum interleukins 8, 4, and 1β levels in patients with gastrointestinal low-grade B-cell lymphoma. (2015)
  • Author(s): Miyata-Takata T, Takata K, Toji T, Goto N, Kasahara S, Takahashi T, Tari A, Noujima-Harada M, Miyata T, Sato Y, Yoshino T.
  • Journal Title: Scientific Reports Volume: 5 Issue: 1 Pages: 18434-18434
  • DOI: 10.1038/srep18434
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Self-consistent field model simulations for statistics of amorphous polymer chains in crystalline lamellar structures (2014)
  • Author(s): T. Uneyama, T. Miyata, K. Nitta
  • Journal Title: The Journal of Chemical Physics Volume: 141 Issue: 16 Pages: 164906-164906
  • DOI: 10.1063/1.4899047
  • Peer Reviewed
• [Journal Article] A numerical approach to surface Green's functions via generalized eigenvalue problems (2013)
  • Author(s): T. Miyata, S. Honda, R. Naito and S.-L. Zhang
  • Journal Title: Japan Journal of Industrial and Applied Mathematics Volume: 30 Issue: 3 Pages: 653-660
  • DOI: 10.1007/s13160-013-0116-2
  • NAID: 210000173856
  • Peer Reviewed
• [Journal Article] An interior eigenvalue problem from electronic structure calculations (2013)
  • Author(s): D. Lee, T. Miyata, T. Sogabe, T. Hoshi and S.-L. Zhang
  • Journal Title: Japan Journal of Industrial and Applied Mathematics Volume: 30 Issue: 3 Pages: 625-633
  • DOI: 10.1007/s13160-013-0118-0
  • NAID: 210000179354
  • Peer Reviewed
• [Journal Article] A numerical approach to surface Green's functions via generalized eigenvalue problems (2013)
  • Author(s): Takafumi Miyata, Syuta Honda, Ryohei Naito, Shao-Liang Zhang
  • Journal Title: Japan Journal of Industrial and Applied Mathematics Volume: 未定
  • NAID: 210000173856
  • Peer Reviewed
• [Presentation] Riccati法に基づくページランク計算 (2015)
  • Author(s): 宮田考史
  • Organizer: RIMS研究集会「現象解明に向けた数値解析学の新展開」
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2015-11-20
  • Invited
• [Presentation] GPUを用いたマルチシフトQR法とその性能最適化 (2014)
  • Author(s): 西澤慶亮, 宮田考史
  • Organizer: 日本応用数理学会「行列・固有値問題の解法とその応用」研究部会第18回研究会
  • Place of Presentation: 東京大学, 東京
  • Year and Date: 2014-12-25
• [Presentation] 重み付きプロクラステス距離を用いたエッシャー風タイリング生成 (2014)
  • Author(s): 川出静, 西澤慶亮, 宮田考史, 今堀慎治
  • Organizer: NICOGRAPH 2014
  • Place of Presentation: 愛知工業大学, 愛知
  • Year and Date: 2014-11-04
• [Presentation] マルチシフトQR法のGPUによる高速化 (2014)
  • Author(s): 宮田考史, 西澤慶亮
  • Organizer: 第3回岐阜数理科学研究会
  • Place of Presentation: 飛騨高山まちの博物館, 岐阜
  • Year and Date: 2014-09-08
• [Presentation] GPUを用いたマルチシフトQR法の高速化について (2014)
  • Author(s): 西澤慶亮, 宮田考史, 張紹良
  • 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
  • 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
• [Presentation] GPUを用いたマルチシフトQR法の高速化について (2014)
  • Author(s): 西澤慶亮, 宮田考史, 張紹良
  • Organizer: 第43回数値解析シンポジウム
  • Place of Presentation: ホテル日航八重山, 沖縄
  • Year and Date: 2014-06-12
• [Presentation] 単位円周上の固有値計算 - Sakurai-Sugiura 法と射影法の利用 - (2014)
  • Author(s): 成瀬由基, 宮田考史, 張紹良
  • Organizer: 第43回数値解析シンポジウム
  • Place of Presentation: ホテル日航八重山, 沖縄
  • Year and Date: 2014-06-12
• [Presentation] GPUを用いたマルチシフトQR法の高速化
  • Author(s): 西澤慶亮，宮田考史，張紹良
  • Organizer: 第42回数値解析シンポジウム
  • Place of Presentation: 四国道後舘，愛媛
• [Presentation] 中間固有値問題とその数値解法
  • Author(s): 李東珍，宮田考史，星健夫，張紹良
  • Organizer: 第42回数値解析シンポジウム
  • Place of Presentation: 四国道後舘，愛媛
• [Presentation] An interior eigenvalue problem and its numerical solution
  • Author(s): D. Lee, T. Miyata, T. Hoshi, S.-L. Zhang
  • Organizer: The 9th East Asia SIAM Conference & The 2nd Conference on Industrial and Applied Mathematics
  • Place of Presentation: Bandung, Indonesia
• [Presentation] 固有値計算のためのマルチシフトQR法 - GPU向けの改良 -
  • Author(s): 西澤慶亮，宮田考史
  • Organizer: 第5回協定講座シンポジウム「計算科学 次代を担う若手の集い 2013」
  • Place of Presentation: 神戸大学統合研究拠点 コンベンションホール，神戸
• [Presentation] 大規模固有値問題に対するJacobi-Davidson法について
  • Author(s): 宮田考史
  • Organizer: RIMS研究集会「応用数理と計算科学における理論と応用の融合」
  • Place of Presentation: 京都大学 益川ホール，京都
• [Presentation] PageRank計算に現れる固有値問題とその数値解法
  • Author(s): 宮田考史
  • Organizer: 第11回計算数学研究会
  • Place of Presentation: ブランナールみささ，鳥取
  • Invited
• [Presentation] Riccati method for PageRank
  • Author(s): T. Miyata
  • Organizer: 2013 NCTS Workshop on Numerical Linear Algebra and High Performance Computing
  • Place of Presentation: Hsinchu, Taiwan
  • Invited
• [Presentation] Computing surface Green's functions
  • Author(s): T. Miyata, R. Naito, S. Honda
  • Organizer: International Workshop on Eigenvalue Problems: Algorithms; Software and Applications, in Petascale Computing
  • Place of Presentation: Tsukuba, Japan
• [Presentation] A numerical approach to interior eigenvalue problems in electronic structure calculations
  • Author(s): D. Lee, T. Miyata, T. Sogabe, T. Hoshi, S.-L. Zhang
  • Organizer: International Workshop on Eigenvalue Problems: Algorithms; Software and Applications, in Petascale Computing
  • Place of Presentation: Tsukuba, Japan
• [Presentation] Jacobi-Davidson Type Methods Using a Shift Invariance Property of Krylov Subspaces for Eigenvalue Problems
  • Author(s): Takafumi Miyata, Tomohiro Sogabe, Shao-Liang Zhang
  • Organizer: SIAM Conference on Applied Linear Algebra
  • Place of Presentation: Valencia, Spain
• [Presentation] 指定された絶対値を有する複素固有値の計算について
  • Author(s): 宮田考史，張紹良
  • Organizer: RIMS研究集会「次世代計算科学の基盤技術とその展開」
  • Place of Presentation: 京都大学数理解析研究所
• [Presentation] PageRank計算に現れる固有値問題の解法について
  • Author(s): 宮田考史，三森浩平
  • Organizer: 日本応用数理学会2013年研究部会連合発表会
  • Place of Presentation: 東洋大学