大規模行列の固有値問題：演算と通信を同時に最小化する世界初の数値解法

2015 Fiscal Year Annual Research Report

• Project/Area Number: 26870149
• Research Institution: The University of Tokyo
• Principal Investigator: 中務 佑治 東京大学, 情報理工学(系)研究科, 助教 (10723554)
• Project Period (FY): 2014-04-01 – 2016-03-31
• Keywords: 固有値アルゴリズム / 固有値の他の分野への応用 / 国際交流、アメリカ

Outline of Annual Research Achievements

申請タイトルの固有値分解アルゴリズムについてはカリフォルニア大学デービス校のRoland Freund教授との共著論文が応用数理の分野では最も権威のある論文誌といえるSIAM Reviewの受理された．研究結果をMITでの招待講演やSIAM ALA conferenceで発表した．
またマンチェスター大学のStefan Guettel氏との共著で行列指数関数の計算アルゴリズムの論文を書き、SIAM journal on Matrix analysis and applicationsに出版された．
その他にも行列固有値を使った数理最適化問題の数値解法を進展させ、論文にして投稿中である．固有値を用いた関数近似論アルゴリズムの論文も執筆中である．
他にもJSIAM Letters,EPASA学会会議録などに出版した．
国際交流という意味ではJared Aurentz,Vladimir Kostic,Robert Luce氏を招聘してセミナー講演とともに研究議論をした．

Research Products

• [Int'l Joint Research] MIT(米国)
  • Country Name: U.S.A.
  • Counterpart Institution: MIT
• [Int'l Joint Research] Univ. Novi Sad(セルビア)
  • Country Name: SERBIA
  • Counterpart Institution: Univ. Novi Sad
• [Int'l Joint Research] EPFL(スイス)
  • Country Name: SWITZERLAND
  • Counterpart Institution: EPFL
• [Int'l Joint Research] Oxford(英国)
  • Country Name: UNITED KINGDOM
  • Counterpart Institution: Oxford
• [Journal Article] Roundoff error analysis of the CholeskyQR2 algorithm in an oblique inner product, (2915)
  • Author(s): Yusaku Yamamoto, Yuji Nakatsukasa, Yuka Yanagisawa and Takeshi Fukaya,
  • Journal Title: JSIAM Letters Volume: 8 Pages: 5-8
  • DOI: http://doi.org/10.14495/jsiaml.8.5
  • Peer Reviewed
• [Journal Article] Computing Fundamental Matrix Decompositions Accurately via the Matrix Sign Function in Two Iterations: The Power of Zolotarev's Functions (2016)
  • Author(s): Yuji Nakatsukasa, Roland W. Freund
  • Journal Title: SIAM Review Volume: TBD Pages: TBD
  • DOI: TBD
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Scaled and squared subdiagonal Pade approximation for the matrix exponential (2016)
  • Author(s): Stefan Guettel, Yuji Nakatsukasa
  • Journal Title: SIAM Journal on Matrix Analysis and Applications Volume: 37 Pages: 145-170
  • DOI: 10.1137/15M1027553
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Presentation] Beest L1 polynomial approximation (2016)
  • Author(s): Yuji Nakatsukasa
  • Organizer: Oxford University Numerical Analysis seminar
  • Place of Presentation: Oxford, UK
  • Year and Date: 2016-04-19 – 2016-04-19
  • Int'l Joint Research
• [Presentation] Matrix Eigenvalue Problems: Theory and Applications (2016)
  • Author(s): Yuji Nakatsukasa
  • Organizer: Stanford University Interview
  • Place of Presentation: Stanford, USA
  • Year and Date: 2016-04-13 – 2016-04-15
  • Int'l Joint Research / Invited
• [Presentation] “Stable polefinding and rational least-squares fitting via eigenvalues”, (2016)
  • Author(s): Yuji Nakatsukasa
  • Organizer: Workshop on Numerical Algebra, Algorithms, and Analysis
  • Place of Presentation: NII, 東京都・千代田区
  • Year and Date: 2016-01-11 – 2016-01-12
  • Int'l Joint Research / Invited
• [Presentation] Computing Fundamental Matrix Decompositions Accurately via the Matrix Sign Function in Two Iterations: The Power of Zolotarev’s Functions (2015)
  • Author(s): Yuji Nakatsukasa
  • Organizer: MIT applied mathematics seminar
  • Place of Presentation: MIT, USA
  • Year and Date: 2015-10-30 – 2015-11-02
  • Int'l Joint Research / Invited
• [Presentation] “Finding a low-rank basis in a matrix subspace” (2015)
  • Author(s): Yuji Nakatsukasa
  • Organizer: Low-rank Optimization and Applications workshop,
  • Place of Presentation: Bonn, Germany
  • Year and Date: 2015-06-08 – 2015-06-12
  • Int'l Joint Research / Invited