Development of Innovative Library for Singular Value Decomposition Suited to Multi-Core Processors

• Project/Area Number: 20246027
• Research Category: Grant-in-Aid for Scientific Research (A)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Engineering fundamentals
• Research Institution: Kyoto University
• Principal Investigator: NAKAMURA Yoshimasa 京都大学, 情報学研究科, 教授 (50172458)
• Co-Investigator(Kenkyū-buntansha): TSUJIMOTO Satoshi 京都大学, 大学院・情報学研究科, 准教授 (60287977) ; KIMURA Kinji 京都大学, 大学院・情報学研究科, 特定准教授 (10447899) ; YAMAMOTO Yusaku 神戸大学, 大学院・システム情報学研究科, 教授 (20362288) ; IWASAKI Masahi 京都府立大学, 大学院・生命環境科学研究科, 准教授 (30397575) ; TAKATA Masami 奈良女子大学, 大学院・人間文化研究科, 助教 (20397574)
• Project Period (FY): 2008 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥27,690,000 (Direct Cost: ¥21,300,000、Indirect Cost: ¥6,390,000); Fiscal Year 2011: ¥7,410,000 (Direct Cost: ¥5,700,000、Indirect Cost: ¥1,710,000); Fiscal Year 2010: ¥8,970,000 (Direct Cost: ¥6,900,000、Indirect Cost: ¥2,070,000); Fiscal Year 2009: ¥11,310,000 (Direct Cost: ¥8,700,000、Indirect Cost: ¥2,610,000)
• Keywords: 数理工学(数理的解析・計画・設計・最適化) / 特異値分解 / マルチコアプロセッサ / 特異値計算 / 原点シフト戦略 / GPGPU / 並列計算 / ライブラリ / クラウドコンピューティング / ライブラリー / 可積分系 / 計算アルゴリズム / ダルブ変換 / グラフィックスプロセッサ / 単精度GPU / 倍精度GPU / GPU / 原点シフト

Research Abstract

This project obtains the following fruits in parallel computations with multi-core CPU environments. 1) A shift strategy based on the generalized Newton shift is completed for computing bidiagonal singular values by the mdLVs. 2) A speed up is established in reorthogonalization of singular vectors by using the Householder transformation with the compact WY representation. 3) A speed up of preconditioning process from given dense matrix to bidiagonal is performed. 4) Evaluation both of performance and accuracy of some singular value decomposition algorithms including I-SVD and D & C in double precision computation in GPGPU are discussed. 5) New integrable algorithms for computing eigenvalues and singular values of some class of band matrices are designed. The resulting code DBDSLV of the fast I-SVD algorithm in terms of 1)-4) can be downloaded in the web page as well as many presentations have been given in international workshops and annual meetings and many research papers have been published.

Research Products

• [Journal Article] Subtraction-free recurrence relations for lower bounds of the minimal singular value of an upper bidiagonal matrixx (2012)
  • Author(s): Takumi Yamashita, Kinji Kimura, and Yoshimasa Nakamura
  • Journal Title: J. Math-for-Industry Volume: Vol.4 Pages: 55-71
• [Journal Article] Subtraction-free recurrence relations for lower bounds of the minimal singular value of an upper bidiagonal matrix (2012)
  • Author(s): Takumi Yamashita, Kinji Kimura, Yoshimasa Nakamura
  • Journal Title: J.Math-for-Industry Volume: 4 Pages: 55-71
  • NAID: 40019493178
  • Peer Reviewed
• [Journal Article] Backward error analysis of the AllReduce algorithm for householder QR decomposition (2012)
  • Author(s): Daisuke Mori, Yusaku Yamamoto, Shao-Liang Zhang
  • Journal Title: Japan Journal of Industrial and Applied Mathematio Volume: 29 Pages: 111-130
  • NAID: 10030213956
  • Peer Reviewed
• [Journal Article] Positivity of dLV and mdLVs algorithms for computing singular values (2011)
  • Author(s): Masashi Iwasaki and Yoshimasa Nakamura
  • Journal Title: Elect. Trans. Numer. Anal Volume: Vol.38 Pages: 184-201
• [Journal Article] Conserved quantities of the discrete finite Toda equation and lower bounds of the minimal singular value of upper bidiagonal matrices (2011)
  • Author(s): Kinji Kimura, Takumi Yamashita and Yoshimasa Nakamura
  • Journal Title: J. Phys. A : Math. Theor Volume: Vol.44 Pages: 285207-285207
• [Journal Article] On auto-tuned pre/post processing for the singular value decomposition of dense square matrices (2011)
  • Author(s): Hiroki Toyokawa, Kinji Kimura, Yusaku Yamamoto, Masami Takata, Akira Ajisaka, Yoshimasa Nakamura
  • Journal Title: 情報処理学会論文誌コンピューティングシステム(ACS) Volume: Vol.4No.3 Pages: 9-21
  • NAID: 130000654785
• [Journal Article] Optimization of the multishift QR algorithm with coprocessors for non-Hermitian eigenvalue problems (2011)
  • Author(s): Takafumi Miyata, Yusaku Yamamoto, Takashi Uneyama, Yoshimasa Nakamura and Shao-Liang Zhang
  • Journal Title: East Asian J. Appl. Math Volume: Vol.1, No.2 Pages: 187-196
• [Journal Article] An improved shift strategy for the modified discrete Lotka-Volterra with shift algorithm (2011)
  • Author(s): Masami Takata, Takumi Yamashita, Akira Ajisaka, Kinji Kimura and Yoshimasa Nakamura
  • Journal Title: Proceedings of The 2011 International Conference on Parallel and Distributed Processing Techniques and Applications(PDPTA2011) Volume: Vol.II Pages: 720-726
• [Journal Article] Implementation and performance evaluation of new inverse iteration algorithm with Householder transformation in terms of the compact WY representation (2011)
  • Author(s): Hiroyuki Ishigami, Kinji Kimura and Yoshimasa Nakamura
  • Journal Title: Proceedings of The 2011 International Conference on Parallel and Distributed Processing Techniques and Applications(PDPTA2011) Volume: Vol.II Pages: 775-780
• [Journal Article] Positivity of dLV and mdLVs algorithms for computing singular values (2011)
  • Author(s): Masashi Iwasaki, Yoshimasa Nakamura
  • Journal Title: Elect.Trans.Numer.Anal. Volume: 38 Pages: 184-201
  • Peer Reviewed
• [Journal Article] Conserved quantities of the discrete finite Toda equation and lower bounds of the minimal singular value of upper bidiagonal matrices (2011)
  • Author(s): Kinji Kimura, Takumi Yamashita, Yoshimasa Nakamura
  • Journal Title: J.Phys.A : Math.Theor. Volume: 44 Issue: 28 Pages: 285207-285207
  • DOI: 10.1088/1751-8113/44/28/285207
  • Peer Reviewed
• [Journal Article] On auto-tuned pre/postprocessing for the singular value decomposition of dense square matrices (2011)
  • Author(s): H.Toyokawa, K.Kimura, Y.Yamamoto, M.Takata, A.Ajisaka, Y.Nakamura
  • Journal Title: 情報処理学会論文誌コンピューティングシステム(ACS) Volume: 4 Pages: 9-21
  • NAID: 130000654785
  • Peer Reviewed
• [Journal Article] A parallel algorithm for incremental orthogonalization based on the compact WY representation (2011)
  • Author(s): Yusaku Yamamoto, Yusuke Hirota
  • Journal Title: JSIAM Letters Volume: 3 Pages: 89-92
  • NAID: 130002129403
  • Peer Reviewed
• [Journal Article] Positivity of dLV and mdLVs Algorithms for Computing Singular Values (2011)
  • Author(s): Masashi Iwasaki, Yoshimasa Nakamura
  • Journal Title: Elect.Trans.Numer.Anal.
  • Peer Reviewed
• [Journal Article] A B"acklund transformation between two integrable discrete hungry systems (2011)
  • Author(s): A.Fukuda, Y.Yamamoto, M.Iwasaki, E.Ishiwata, Y.Nakamura
  • Journal Title: Phys.Lett.A Volume: 375 Pages: 303-308
  • Peer Reviewed
• [Journal Article] On condition numbers in the cyclic reduction processes of a tridiagonal matrix (2010)
  • Author(s): Tan Wang, Masashi Iwasaki and Yoshimasa Nakamura
  • Journal Title: Intern. J. of Computer Math Volume: Vol.87 Pages: 3079-3093
• [Journal Article] 密正方行列特異値分解における並列I-SVD法の特性を用いた後処理の高速化 (2010)
  • Author(s): 豊川博己, 山本有作, 木村欣司, 高田雅美, 中村佳正
  • Journal Title: 情報処理学会論文誌コンピューティングシステム(ACS) Volume: Vol.3, No.2 Pages: 30-38
  • NAID: 110007990289
• [Journal Article] 特異値分解アルゴリズムの性能評価のための2重対角テスト行列生成アルゴリズム (2010)
  • Author(s): 高田雅美, 木村欣司, 中村佳正
  • Journal Title: 情報処理学会研究報告MPS,数理モデル化と問題解決研究報告 Volume: MPS-79(1) Pages: 1-6
• [Journal Article] Generating algorithms for matrices with large condition number to evaluate singular value decomposition (2010)
  • Author(s): Masami Takata, Kinji Kimura and Yoshimasa Nakamura
  • Journal Title: Proceedings of The 2010 International Conference on Parallel and Distributed Processing Techniques and Applications(PDPTA2010) Volume: Vol.II Pages: 619-625
  • NAID: 110007993905
• [Journal Article] 密正方行列特異値分解における並列I-SVD法の特性を用いた後処理の高速化 (2010)
  • Author(s): 豊川博己, 山本有作, 木村欣司, 高田雅美, 中村佳正
  • Journal Title: 情報処理学会論文誌コンピューティングシステム(ACS) 3巻,No.2 Pages: 30-38
  • NAID: 110007990289
  • Peer Reviewed
• [Journal Article] Differential qd Algorithm for Totally Nonnegative Hessenberg Matrices : Introduction of Origin Shifts and Relationship with the Discrete Hungry Lotka-Volterra System (2010)
  • Author(s): Y.Yamamoto, T.Fukaya
  • Journal Title: JSIAM Letters Volume: Vol.2 Pages: 69-72
  • NAID: 130000303923
  • Peer Reviewed
• [Journal Article] Exceptional Laguerre and Jacobi polynomials and the corresponding potentials through Darboux-Crum transformations (2010)
  • Author(s): R.Sasaki, S.Tsujimoto, A.Zhedanov
  • Journal Title: Journal of Physics A : Mathematical and theoretical Volume: 43
  • Peer Reviewed
• [Journal Article] Performance Modeling of Multishift QR Algorithms for the Parallel Solution of Symmetric Tridiagonal Eigenvalue Problems (2010)
  • Author(s): T.Miyata, Y.Yamamoto, S.-L.Zhang
  • Journal Title: Lecture Notes in Computer Science(Springer) Volume: No.6082 Pages: 401-412
  • Peer Reviewed
• [Journal Article] 階層的な性能モデルに基づく行列計算の自動チューニング (2010)
  • Author(s): 山本有作, 深谷猛
  • Journal Title: 応用数理 Volume: Vol.20, No.3 Pages: 15-25
  • Peer Reviewed
• [Journal Article] 密正方行列特異値分解における並列I-SVD法の特性を用いた後処理の高速化 (2010)
  • Author(s): 豊川博己, 山本有作, 木村欣司, 高田雅美, 中村佳正
  • Journal Title: 情報処理学会論文誌 コンピューティングシステム(ACS) Volume: Vol.3.No.2 Pages: 30-38
  • NAID: 110007990289
  • Peer Reviewed
• [Journal Article] On parallelism of the I-SVD algorithm with multi-core processor (2009)
  • Author(s): Hiroki Toyokawa, Kinji Kimura, Masami Takata and Yoshimasa Nakamura
  • Journal Title: JSIAM Lett Volume: Vol.1 Pages: 48-51
  • NAID: 130000133091
• [Journal Article] A new algorithm for singular value decomposition and its parallelization (2009)
  • Author(s): Taro Konda and Yoshimasa Nakamura
  • Journal Title: Parallel Computing Volume: Vol.35 Pages: 331-344
• [Journal Article] On parallelization of the I-SVD algorithm and its evaluation for clustered singular values (2009)
  • Author(s): Hiroki Toyokawa, Kinji Kimura, Masami Takata and Yoshimasa Nakamura
  • Journal Title: Proceedings of The 2009 International Conference on Parallel and Distributed Processing Techniques and Applications(PDPTA2009) Volume: Vol.II Pages: 711-717
  • NAID: 110007993815
• [Journal Article] Speed-up in mdLVs by limitation in computational number of shift (2009)
  • Author(s): Masami Takata, Kinji Kimura and Yoshimasa Nakamura
  • Journal Title: Proceedings of The 2009 International Conference on Parallel and Distributed Processing Techniques and Applications(PDPTA2009) Volume: Vol.II Pages: 704-710
  • NAID: 110007993814
• [Journal Article] On parallelism of the I-SVD algorithm with multi-core processor (2009)
  • Author(s): Hiroki Toyokawa, Kinji Kimura, Masami Takata, Yoshimasa Nakamura
  • Journal Title: JSIAM Lett. Vol.1 Pages: 48-51
  • NAID: 130000133091
  • Peer Reviewed
• [Journal Article] 正方行列向け特異値分解のCUDAによる高速化 (2009)
  • Author(s): 深谷猛, 山本有作, 畝山多加志, 中村佳正
  • Journal Title: 情報処理学会論文誌 コンピューティングシステム(ACS) 2巻,No.2 Pages: 98-109
  • NAID: 110007990234
  • Peer Reviewed
• [Journal Article] A new algorithm for singular value decomposition and its parallelization (2009)
  • Author(s): Taro Konda, Yoshimasa Nakamura
  • Journal Title: Parallel Computing Vol.35 Pages: 331-344
  • Peer Reviewed
• [Journal Article] 多倍長環境における最適PWM問題の数値解法 (2009)
  • Author(s): 矢谷健一, 木村欣司, 中村佳正
  • Journal Title: 日本応用数理学会論文誌 19 Pages: 105-120
  • NAID: 110007162160
  • Peer Reviewed
• [Journal Article] 特異値分解法I-SVDにおける左特異ベクトル計算部の改善 (2008)
  • Author(s): 片山幹基, 木村欣司, 高田雅美, 坪井洋明, 岩崎雅史, 中村佳正
  • Journal Title: 日本応用数理学会論文誌 18 Pages: 389-407
  • Peer Reviewed
• [Journal Article] 固有値分解を目的としたツイスト分解法による分割統治法の改善 (2008)
  • Author(s): 坪井洋明, 誉田太朗, 岩崎雅史, 木村欣司, 高田雅美, 中村佳正
  • Journal Title: 日本応用数理学会論文誌 18 Pages: 611-630
  • Peer Reviewed
• [Presentation] Some aspects of the integrable discrete Lotka-Volterra system (2011)
  • Author(s): Masashi Iwasaki, Yoshimasa Nakamura
  • Organizer: International Conference on Scientific Computing (SC2011)
  • Place of Presentation: Cagliari(イタリア)(招待講演)
  • Year and Date: 2011-10-13
• [Presentation] An improved shift strategy for the modified discrete Lotka-Volterra with shift algorithm (2011)
  • Author(s): Masami Takata, Takumi Yamashita, Akira Ajisaka, Kinji Kimura, Yoshimasa Nakamura
  • Organizer: The 2011 International Conference on Parallel and Distributed Processing Techniques and Applications (PDPTA2011)
  • Place of Presentation: Monte Carlo Resort, Las Vegas(アメリカ)
• [Presentation] On an implementation of new inverse iteration algorithm with Householder transformation in terms of the compact WY representation and its performance evaluation (2011)
  • Author(s): Hiroyuki Ishigami, Kinji Kimura, Yoshimasa Nakamura
  • Organizer: The 2011 International Conference on Parallel and Distributed Processing Techniques and Applications (PDPTA2011)
  • Place of Presentation: Monte Carlo Resort, Las Vegas(アメリカ)
• [Presentation] Acceleration of Hessenberg Reduction for Nonsymmetric Eigenvalue Problems Using GPU (2010)
  • Author(s): J.Muramatsu, Y.Yamamoto, S.-L.Zhang
  • Organizer: First International Conference on Networking and Computing (ICNC 2010)
  • Place of Presentation: 広島
  • Year and Date: 2010-11-19
• [Presentation] 非線形可積分系に基づく高精度特異値計算アルゴリズムmdLVsの開発について (2010)
  • Author(s): 中村佳正
  • Organizer: 計測自動制御学会 第39回制御理論シンポジウム
  • Place of Presentation: ホテルコスモスクエア国際交流センター(特別講演)
• [Presentation] Integrable algorithms : from Moser to I-SVD (2010)
  • Author(s): Yoshimasa Nakamura
  • Organizer: Symmetry Plus Integrability 2010 (SPI2010), The First International Conference on Integrable Systems and Nonlinear Waves on the Gulf of Mexico (plenary talk)
  • Place of Presentation: South Padre Island, USA
• [Presentation] 非線形可積分系に基づく高精度特異値計算アルゴリズムmdLVsの開発について (2010)
  • Author(s): 中村佳正
  • Organizer: 計測自動制御学会第39回制御理論シンポジウム
  • Place of Presentation: ホテルコスモスクエア国際交流センター
• [Presentation] 可積分アルゴリズム (2009)
  • Author(s): 中村佳正
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 大阪大学(企画特別講演)
• [Presentation] On parallelization of the I-SVD algorithm and its evaluation for clustered singular values (2009)
  • Author(s): H. Toyokawa, K. Kimura, M. Takata, Yoshimasa Nakamura
  • Organizer: Proceedings of The 2009 International Conference on Parallel and Distributed Processing Techniques and Applications (PDPTA2009), Vol.II, pp.711-717
  • Place of Presentation: Las Vegus, USA
• [Presentation] 正方行列向け特異値分解のCUDAによる高速化 (2009)
  • Author(s): 深谷猛, 山本有作, 畝山多加志, 中村佳正
  • Organizer: 情報処理学会 2009年ハイパフオーマンスコンピューテイングと計算科学シンポジウム
  • Place of Presentation: 東京大学武田ホール
• [Presentation] Parallel double divide and conquer and its evaluation on a multi-core computer (2008)
  • Author(s): T. Konda, H. Toyokawa, Y. Nakamura
  • Organizer: The IADIS International Conference Applied Computing 2008
  • Place of Presentation: Carvoeiro, Portugal
• [Presentation] 純国産特異値分解アルゴリズムI-SVDとその可能性 (2008)
  • Author(s): 中村佳正
  • Organizer: 情報学会研究発表講演会
  • Place of Presentation: 京都情報大学院大学
• [Presentation] Evaluations of parallel double divide and conquer on a 16. core computer (2008)
  • Author(s): T. Konda, H. Toyokawa, Y. Nakamura
  • Organizer: The International Conference on Parallel and Distributed Processing Techniques and Applications (PDPTA2008)
  • Place of Presentation: Monte Carlo Resort, Las Vegas
• [Book] 「並列数値処理」第6章「高速フーリエ変換」金田康正(編著) (2010)
  • Author(s): 山本有作
  • Total Pages: 272
  • Publisher: コロナ社
• [Book] Software Automatic Tuning : From Concepts to the State-of-the-Art Results", Chapter 5, "Dynamic Programming Approaches to Optimizing the Blocking Strategy for Basic Matrix Decompositions"(K.Naono, K.Teranishi, J.Cavazos and R.Suda (eds.))" (2010)
  • Author(s): Y.Yamamoto, T.Fukaya
  • Total Pages: 240
  • Publisher: Springer
• [Remarks] ソフトウェアの公開(1)倍精度2重対角行列特異値分解ルーチンDBDSLV2010の公開
  • URL: http://www-is.amp.i.kyoto-u.ac.jp/svd/index.html
• [Remarks] (2)倍精度2重対角行列シフト付き用特異値計算ルーチンDLVS2010の公開
  • URL: http://www-is.amp.i.kyoto-u.ac.jp/svd/index.html
• [Remarks]
  • URL: http://www-is.amp.i.kyoto-u.ac.jp/svd/index.html
• [Remarks] ホームページ公開中の成果ソフトウェア
  • URL: http://www-is.amp.i.kyoto-u.ac.jp/lab/isvd/
• [Remarks] 倍精度2重対角行列シフト付き用特異値計算ルーチンDLVS
• [Remarks] 倍精度2重対角行列特異値分解ルーチンDBDSLV
• [Remarks]
  • URL: http://www-is.amp.i.kyoto-u.ac.jp/svd/index.html
• [Remarks]
  • URL: http://www-is.amp.i.kyoto-u.ac.jp/svd/index.html
• [Remarks]
  • URL: http://www-is.amp.i.kvoto-u.ac.jp/lab/isvd/
• [Patent(Industrial Property Rights)] 画像特徴抽出方法および画像圧縮方法 (2010)
  • Inventor(s): 中村佳正、岩崎雅史、小幡雅彦、近藤弘一、笹田昇
  • Industrial Property Rights Holder: 科学技術振興機構、同志社大学
  • Industrial Property Number: 2006-211219
  • Acquisition Date: 2010-12-24
• [Patent(Industrial Property Rights)] 行列の高速高精度特異値分解法、プログラムおよび装置 (2009)
  • Inventor(s): 中村佳正、岩崎雅史、阪野真也
  • Industrial Property Rights Holder: 科学技術振興機構
  • Acquisition Date: 2009-06-19
• [Patent(Industrial Property Rights)] SINGULAR VALUE DECOMPOSITION DEVICE AND SINGULAR VALUE DECOMPOSITION METHOD (2008)
  • Inventor(s): Nakamura Yoshimasa, Konda Taro, Iwasaki Masashi, Sakano Shinya, Takata Masami
  • Industrial Property Rights Holder: JST
  • Filing Date: 2008-06-04
  • Overseas