Fast and accurate eigenvalue solver for many-core processors

• Project/Area Number: 21560065
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Engineering fundamentals
• Research Institution: Kobe University
• Principal Investigator: YAMAMOTO Yusaku 神戸大学, 大学院・システム情報学研究科, 教授 (20362288)
• Project Period (FY): 2009 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000); Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2009: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
• Keywords: 固有値計算 / 線形計算 / メニーコア / 並列処理 / 固有値問題 / スーパーコンピュータ / ブロックヤコビ法 / 数値計算 / アルゴリズム / マルチコア / 誤差解析 / 直交化 / QR分解

Research Abstract

The objective of this research is to develop efficient algorithms for computing eigenvalues on many-core processors. The achievements of this research can be summarized as follows:
(1) Implementation and performance evaluation of an eigenvalue computation algorithm designed for multi-core/many-core processors
(2) Error analysis of the AllReduce algorithm for Householder QR decomposition
(3) A new highly parallel algorithm for incremental orthogonalization
(4) A new algorithm for computing the eigenvalues of a totally nonnegative band Hessenberg matrix with high relative accuracy

Research Products

• [Journal Article] On a shifted LR transformation derived from the discrete hungry Toda equation (2013)
  • Author(s): Akiko Fukuda, Yusaku Yamamoto, Masashi Iwasaki, Emiko Ishiwata and Yoshimasa Nakamura
  • Journal Title: Monatshefte Fuer Mathematik Volume: Vol. 170, No. 1 Pages: 11-26
  • Peer Reviewed
• [Journal Article] On a shifted LR transformation derived from the discrete hungry Toda equation (2013)
  • Author(s): A. Fukuda, Y. Yamamoto, M. Iwasaki, E. Ishiwata and Y. Nakamura
  • Journal Title: Monatsh Math. Volume: 170 Issue: 1 Pages: 11-26
  • DOI: 10.1007/s00605-012-0404-y
  • Peer Reviewed
• [Journal Article] Backward error analysis of the AllReduce algorithm for householder QR decomposition (2012)
  • Author(s): Daisuke Mori, Yusaku Yamamotoand Shao-Liang Zhang
  • Journal Title: Japan Journal of Industrial and Applied Mathematics Volume: Vol.29, No. 1 Pages: 111-130
  • NAID: 10030213956
  • Peer Reviewed
• [Journal Article] On Some Properties of Discrete Integrable System Derived from Hungry Lotka-Volterra System of Multiplicative Type (2012)
  • Author(s): Yusuke Hama, Akiko Fukuda, Yusaku Yamamoto, Masashi Iwasaki, Emiko Ishiwata and Yoshimasa Nakamura
  • Journal Title: Journal of Math-for-Industry Volume: Vol. 4(A) Pages: 5-15
  • Peer Reviewed
• [Journal Article] Error analysis for matrix eigenvalue algorithm based on the discrete hungry Toda equation (2012)
  • Author(s): Akiko Fukuda, Yusaku Yamamoto, Masashi Iwasaki, Emiko Ishiwata and Yoshimasa Nakamura
  • Journal Title: Numerical Algorithms Volume: Vol. 61, No. 2 Pages: 243-260
  • Peer Reviewed
• [Journal Article] Error analysis for matrix eigenvalue algorithm based on the discrete hungry Toda equation (2012)
  • Author(s): A. Fukuda, Y. Yamamoto, M. Iwasaki, E. Ishiwata and Y. Nakamura
  • Journal Title: Numerical Algorithms Volume: 61 Issue: 2 Pages: 243-260
  • DOI: 10.1007/s11075-012-9606-6
  • Peer Reviewed
• [Journal Article] On Some Properties of Discrete Integrable System Derived from Hungry Lotka-Volterra System of Multiplicative Type (2012)
  • Author(s): Y. Hama, A. Fukuda, Y. Yamamoto, M. Iwasaki, E. Ishiwata and Y. Nakamura
  • Journal Title: Journal of Math-for-Industry Volume: 4(A) Pages: 5-15
  • Peer Reviewed
• [Journal Article] 倍精度正方行列特異値分解アルゴリズムのGPGPU上での性能・精度評価 (2012)
  • Author(s): 廣田悠輔，橋本拓也，山本有作
  • 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: 5 Pages: 163-176
  • NAID: 110009464403
  • Peer Reviewed
• [Journal Article] 非直交同時対角化アルゴリズムのハイブリッド解法 (2012)
  • Author(s): 廣田悠輔，山本有作，張紹良
  • Journal Title: 日本応用数理学会論文誌 Volume: 22 Pages: 63-79
  • NAID: 10031083224
  • Peer Reviewed
• [Journal Article] Cache Optimization of a Non-Orthogonal Joint Diagonalization Method (2011)
  • Author(s): Y. Hirota, Y. Yamamotoand S.-L. Zhang
  • Journal Title: JSIAM Letters Volume: Vol. 3 Pages: 9-12
  • NAID: 130000433790
  • Peer Reviewed
• [Journal Article] Optimization of the Multishift QR Algorithm with Coprocessors for Non-Hermitian Eigenvalue Problems (2011)
  • Author(s): T. Miyata, Y. Yamamoto, T. Uneyama, Y. Nakamura and S.-L. Zhang
  • Journal Title: East Asian Journal on Applied Mathematics Volume: Vol. 1, No. 2 Pages: 187-196
  • Peer Reviewed
• [Journal Article] A Block IDR(s) Method for Nonsymmetric Linear Systems with Multiple Right-Hand Sides (2011)
  • Author(s): L. Du, T. Sogabe, B. Yu, Y. Yamamotoa n d S.-L. Zhang
  • Journal Title: Journal of Computational and Applied Mathematics Volume: Vol. 235 Pages: 4095-4106
  • Peer Reviewed
• [Journal Article] A parallel algorithm for incremental orthogonalization based on the compact WY representation (2011)
  • Author(s): Yusaku Yamamotoand Yusuke Hirota
  • Journal Title: JSIAM Letters Volume: Vol. 3 Pages: 89-92
  • NAID: 130002129403
  • Peer Reviewed
• [Journal Article] Acceleration of Hessenberg Reduction for Nonsymmetric Eigenvalue Problems in a Hybrid CPU-GPU Computing Environment (2011)
  • Author(s): Jun-ichi Muramatsu, Shao-Liang Zhang and Yusaku Yamamoto
  • Journal Title: International Journal of Networking and Computing Volume: Vol. 1, No. 2 Pages: 132-143
  • NAID: 130005475258
  • Peer Reviewed
• [Journal Article] A Backlund Transformation Between Two Integrable Discrete Hungry Systems (2011)
  • Author(s): Akiko Fukuda, Yusaku Yamamoto, Masashi Iwasaki, Emiko Ishiwata, Yoshimasa Nakamura
  • Journal Title: Physics Letters A Volume: Vol.375 Pages: 303-308
  • 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] Four-point Correlation Function of a Passive Scalar Field in Rapidly Fluctuating Turbulence: Numerical Analysis of an Exact Closure Equation (2010)
  • Author(s): oshinori Mizuno, Kouhei Ohi, Tomohiro Sogabe, Yusaku Yamamoto, Yukio Kaneda
  • Journal Title: Phys. Rev. E Volume: Vol.82 Pages: 36316-36324
  • 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): Yusaku Yamamoto, Takeshi Fukaya
  • Journal Title: JSIAM Letters Volume: Vol.2 Pages: 69-72
  • NAID: 130000303923
  • 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): Yusaku Yamamoto, Takeshi Fukaya
  • Journal Title: JSIAM Letters Volume: Vol.2 Pages: 69-72
  • NAID: 130000303923
  • Peer Reviewed
• [Journal Article] Four-point Correlation Function of a Passive Scalar Field in Rapidly Fluctuating Turbulence : Numerical Analysis of an Exact Closure Equation (2010)
  • Author(s): Yoshinori Mizuno, Kouhei Ohi, Tomohiro Sogabe, Yusaku Yamamoto, Yukio Kaneda
  • Journal Title: Phys.Rev.E Volume: Vol.82 Pages: 36316-36324
  • Peer Reviewed
• [Journal Article] Backward error analysis of the AllReduce algorithm for householder QR decomposition
  • Author(s): Daisuke Mori, Yusaku Yamamoto, Shao-Liang Zhang
  • Journal Title: Japan Journal of Industrial and Applied Mathematics Volume: (掲載確定)
  • NAID: 10030213956
  • Peer Reviewed
• [Journal Article] On a shifted LR transformation derived from the discrete hungry Toda equation
  • Author(s): Akiko Fukuda, Yusaku Yamamoto, Masashi Iwasaki, Emiko Ishiwata, Yoshimasa Nakamura
  • Journal Title: Monatshefte fur Mathematik Volume: (掲載確定)
  • Peer Reviewed
• [Presentation] Performance Modeling of the Eigen-K Dense Eigensolver on Massively Parallel Machines (2013)
  • Author(s): Takeshi Fukaya, Toshiyuki Imamura and Yusaku Yamamoto
  • Organizer: SIAM Conference on Computational Science and Engineering (CSE13),The Westin Boston Waterfront
  • Place of Presentation: Boston, USA
• [Presentation] Performance Modeling of the Eigen-K Dense Eigensolver on Massively Parallel Machines (2013)
  • Author(s): Takeshi Fukaya, Toshiyuki Imamura and Yusaku Yamamoto
  • Organizer: Conference on Computational Science and Engineering (CSE13)
  • Place of Presentation: Boston
• [Presentation] Performance Evaluation and Tuning of Tall Skinny Type QR Factorization on the K Computer (2013)
  • Author(s): Takeshi Fukaya and Yusaku Yamamoto
  • Organizer: 2013 Conference on Advanced Topics and Auto Tuning in High Performance Scientific Computing
  • Place of Presentation: Taipei
• [Presentation] Cache optimization of a non-orthogonal joint diagonalization method (2012)
  • Author(s): Yusuke Hirota, Yusaku Yamamoto, Shao-Liang Zhang
  • Organizer: SIAM Conference on Parallel Processing 2012
  • Place of Presentation: Hyatt Regency Savannah, Savannah, USA
  • Year and Date: 2012-02-17
• [Presentation] Performance of the Block Jacobi Method for the Symmetric Eigenvalue Problem on a Modern Massively Parallel Computer (2012)
  • Author(s): Yuusuke Takahashi, Yuusuke Hirota and Yusaku Yamamoto
  • Organizer: ALGORITMY 2012
  • Place of Presentation: Podbanske, Slovakia
• [Presentation] An Acceleration of Backward Transformation of Singular Vectors on a CPU and GPU Heterogeneous Environment (2012)
  • Author(s): Yusuke Hirota and Yusaku Yamamoto
  • Organizer: Parallel Matrix Algorithms and Applications 2012, Birkbeck University of London
  • Place of Presentation: London, UK
• [Presentation] Cache optimization of a non-orthogonal joint diagonalization method (2012)
  • Author(s): Yusuke Hirota, Yusaku Yamamoto and Shao-Liang Zhang
  • Organizer: SIAM Conference on Parallel Processing 2012, Hyatt Regency Savannah
  • Place of Presentation: Savannah, USA
• [Presentation] An Acceleration of Backward Transformation of Singular Vectors on a CPU and GPU Heterogeneous Environment (2012)
  • Author(s): Yusuke Hirota and Yamamoto Yamamoto
  • Organizer: Parallel Matrix Algorithms and Applications 2012
  • Place of Presentation: London
• [Presentation] Performance of the Block Jacobi Method for the Symmetric Eigenvalue Problem on a Modern Massively Parallel Computer (2012)
  • Author(s): Yuusuke Takahashi, Yuusuke Hirota and Yusaku Yamamoto
  • Organizer: ALGORITMY 2012
  • Place of Presentation: Podbanske
• [Presentation] Auto-tuning for BLAS-based Matrix Computations (2011)
  • Author(s): Takeshi Fukaya, Yusaku Yamamotoand S.-L. Zhang
  • Organizer: SIAM Conference on Computational Science and Engineering (CSE11), Grand Sierra Resort and Casino
  • Place of Presentation: Reno, Nevada
• [Presentation] Acceleration of Hessenberg Reduction for Nonsymmetric Eigenvalue Problems Using GPU (2010)
  • Author(s): Jun-ichi Muramatsu, Shao-Liang Zhang, Yusaku Yamamoto
  • Organizer: PDAA 2010
  • Place of Presentation: Hiroshima(広島県)
  • Year and Date: 2010-11-19
• [Presentation] Performance Modeling of Multishift QR Algorithms for the Parallel Solution of Symmetric Tridiagonal Eigenvalue Problems (2010)
  • Author(s): Takafumi Miyata, Yusaku Yamamoto, Shao-Liang Zhang
  • Organizer: M2A2 2010
  • Place of Presentation: Busan(韓国)
  • Year and Date: 2010-05-23
• [Presentation] An Approach to Automatic Tuning for the Parallel Householder QR Decomposition (2010)
  • Author(s): akeshi Fukaya, Yusaku Yamamotoand S.-L. Zhang
  • Organizer: SIAM Conference on Parallel Processing for Scientific Computing (PP10), Grand Hyatt Seattle, Seattle
  • Place of Presentation: Washington,(America)
• [Book] 高速フーリエ変換 (金田康正編著: 並列数値処理, 第5 章) (2010)
  • Author(s): 山本有作
  • Publisher: コロナ社
• [Book] Dynamic Programming Approach to Optimizing the Blocking Strategy for Basic Matrix Decompositions, (Ken Naono et al. (eds): Software Automatic Tuning - From Concepts to State-of-the-Art Results, Chapter 5) (2010)
  • Author(s): Yusaku Yamamoto and Takeshi Fukaya
  • Publisher: Springer
• [Book] 「並列数値処理」(金田康正編著)第5章「高速フーリエ変換」 (2010)
  • Author(s): 山本有作
  • Total Pages: 272
  • Publisher: コロナ社
• [Remarks]
  • URL: http://www.na.scitec.kobe-u.ac.jp/~yamamoto/