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Development of high speed singular value decomposition algorithm for sparse matrices of large scale and upload of its source code

Research Project

Project/Area Number 24360038
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypePartial Multi-year Fund
Section一般
Research Field Engineering fundamentals
Research InstitutionKyoto University

Principal Investigator

Nakamura Yoshimasa  京都大学, 情報学研究科, 教授 (50172458)

Co-Investigator(Kenkyū-buntansha) KIMURA Kinji  京都大学, 大学院情報学研究科, 特定准教授 (10447899)
Project Period (FY) 2012-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥18,850,000 (Direct Cost: ¥14,500,000、Indirect Cost: ¥4,350,000)
Fiscal Year 2014: ¥6,500,000 (Direct Cost: ¥5,000,000、Indirect Cost: ¥1,500,000)
Fiscal Year 2013: ¥5,720,000 (Direct Cost: ¥4,400,000、Indirect Cost: ¥1,320,000)
Fiscal Year 2012: ¥6,630,000 (Direct Cost: ¥5,100,000、Indirect Cost: ¥1,530,000)
Keywords特異値分解 / 大規模スパース行列 / Golub-Kahan-Lanczos法 / 部分特異対 / 再直交化 / 部分特異対計算 / 2分法 / 逆反復法 / 並列計算 / Golub-Kahan-Lanczos前処理 / 応用数学 / アルゴリズム / 固有対計算 / 固有値分解 / 実装コード公開
Outline of Final Research Achievements

Singular value decomposition of sparse matrices of large scale is an important matrix operation which is fundamental for analyzing big data. In this research we apply the Golub-Kahan-Lanczos algorithm with reorthogonalization to sparse matrices of large scale to generate approximated tridiagonal matrices by high performance computation in parallel processing. Secondly the bisection and the inverse iteration methods are applied to them to giving a subset of eigenpairs of the originals with high reusability of data. The corresponding source codes have been uploaded one by one. When the sparse matrices are positive definite, then the resulting eigenpairs lead to a sebset of singular triplets.

Report

(5 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Annual Research Report
  • 2013 Annual Research Report
  • 2012 Annual Research Report
  • Research Products

    (45 results)

All 2016 2015 2014 2013 2012 Other

All Journal Article (18 results) (of which Peer Reviewed: 18 results,  Open Access: 8 results,  Acknowledgement Compliant: 1 results) Presentation (24 results) (of which Int'l Joint Research: 2 results,  Invited: 1 results) Remarks (3 results)

  • [Journal Article] A new parallel symmetric tridiagonal eigensolver based on bisection and inverse iteration algorithms for shared-memory multi-core processors2015

    • Author(s)
      Hiroyuki Ishigami, Kinji Kimura and Yoshimasa Nakamura
    • Journal Title

      Proceedings of the 10th International Conference on P2P, Parallel, Grid, Cloud and Internet Computing (3PGCIC-2015)

      Volume: 1 Pages: 216-223

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Performance evaluation of Golub-Kahan-Lanczos algorithm with reorthogonalization by classical Gram-Schmidt algorithm and OpenMP2015

    • Author(s)
      Masami Takata, Hiroyuki Ishigami, Kinji Kimura, Yuki Fujii, Hiroki Tanaka, Yoshimasa Nakamura
    • Journal Title

      Proceedings of The 2015 International Conference on Parallel and Distributed Processing Techniques and Applications (PDPTA2015)

      Volume: 2 Pages: 243-249

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Implementation details of an extended oqds algorithm for singular values2015

    • Author(s)
      Sho Araki, Kinji Kimura, Yusaku Yamamoto and Yoshimasa Nakamura
    • Journal Title

      JSIAM Letters

      Volume: 7 Pages: 9-12

    • NAID

      130004953465

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] A finite-step construction of totally nonnegative matrices with specified eigenvalues2015

    • Author(s)
      Kanae Akaiwa, Yoshimasa Nakamura, Masashi Iwasaki, Hisayoshi Tsutsumi, Koichi Kondo
    • Journal Title

      Numerical Algorithms

      Volume: 未定 Issue: 3 Pages: 469-484

    • DOI

      10.1007/s11075-015-9957-x

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Accurate similarity transformation derived from the discrete Lotka-Volterra system for bidiagonal singularvalues2014

    • Author(s)
      Munehiro Nagata, Masashi Iwasaki and Yoshimasa Nakamura
    • Journal Title

      Journal Calcolo

      Volume: 未定 Issue: 2 Pages: 305-317

    • DOI

      10.1007/s10092-013-0085-5

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] A tridiagonal matrix construction by the quotient difference recursion formula in the case of multiple eigenvalues2014

    • Author(s)
      Kanae Akaiwa, Masashi Iwasaki, Koichi Kondo and Yoshimasa Nakamura
    • Journal Title

      Pacic J. Math. Indust.

      Volume: 6 Pages: 21-29

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] 再直交化付きブロック逆反復法による固有ベクトルの並列計算2014

    • Author(s)
      石上裕之, 木村欣司, 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

      Volume: 7 Pages: 1-12

    • NAID

      110009815415

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Acceleration of numerical computation for positive roots of polynomials by improved bounds2014

    • Author(s)
      Kinji Kimura, Takuto Akiyama, Hiroyuki Ishigami, Masami Takata, Yoshimasa Nakamura
    • Journal Title

      Proceedings of The 2014 International Conference on Parallel and Distributed Processing Techniques and Applications (PDPTA2014)

      Volume: II Pages: 201-207

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] GPU Implementation of Inverse Iteration Algorithm for Computing Eigenvectors2014

    • Author(s)
      Hiroyuki Ishigami, Kinji Kimura, Yoshimasa Nakamura
    • Journal Title

      Proceedings of 2014 22nd Euromicro International Conference on Parallel, Distributed and network-based Processing

      Volume: I Pages: 664-671

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On implementation and evaluation of inverse iteration algorithm with compact WY orthogonalization2013

    • Author(s)
      Hiroyuki Ishigami, Kinji Kimura, Yoshimasa Nakamura
    • Journal Title

      IPSJ Trans. Math. Modeling Appl.

      Volume: 6 Pages: 25-35

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 特異値分解アルゴリズムの性能評価のための大きな条件数を持つ行列作成2013

    • Author(s)
      高田雅美,木村欣司,中村佳正
    • Journal Title

      情報処理学会論文誌, 数理モデル化と応用

      Volume: 6 Pages: 75-86

    • NAID

      110009656646

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 特異値計算アルゴリズムdqds 法およびm2dLVs 法のための新しいシフト戦略2013

    • Author(s)
      高田雅美, 豊川博己, 石上裕之, 木村欣司, 山下巧, 岩崎雅史, 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

      Volume: 6 Pages: 94-107

    • NAID

      110009606663

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Implementation of the orthogonal qd algorithm for lower tridiagonal matrices2013

    • Author(s)
      Sho Araki, Hiroki Tanaka, Kinji Kimura and Yoshimasa Nakamura
    • Journal Title

      Proceedings of The 2013 International Conference on Parallel and Distributed Processing Techniques and Applications

      Volume: II Pages: 161-167

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 特異値分解アルゴリズムの性能評価のための大きな条件数を持つ行列作成2013

    • Author(s)
      高田雅美, 木村欣司, 中村佳正
    • Journal Title

      情報処理学会,MPS-PDPTAI0-2, TOM

      Volume: (掲載確定)(印刷中)

    • NAID

      110009656646

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On implementation and evaluation of inverse iteration algorithm with compact WY orthogonalizat ion2013

    • Author(s)
      Hiroyuki Ishigami, Kinji Kimura, Yoshimasa Nakamura
    • Journal Title

      情報処理学会, MPS-PDPTA11-8, TOM

      Volume: (掲載確定)

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 特異値計算アルゴリズムdqds法およびmdLVs法のための新しいシフト戦略,2013

    • Author(s)
      高田雅美, 石上裕之, 木村欣司, 山下巧, 岩崎雅史, 中村佳正
    • Journal Title

      情報処理学会,ハイパフォーマンスコンピューティングと計算科学シンポジウム論文集(掲載確定)

      Volume: (掲載確定)(印刷中)

    • NAID

      170000073607

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Accelerating the reorthogona1i za t i on on singular vectors with a multi-coreprocessor2013

    • Author(s)
      Hiroki Toyokawa, Hiroyuki Ishigami, Kinji Kimura, Masami Takata and Yoshimasa Nakamura
    • Journal Title

      Lecture Notes in Computer Science (LNCS), Springer - Verlag,

      Volume: (掲載確定)(印刷中)

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] An application of the Kato-Temple inequality on matrix eigenvalues to the dqds algorithm for singular values2013

    • Author(s)
      Takumi Yamashita, Kinji Kimura, and Yoshimasa Nakamura
    • Journal Title

      JSIAM Letters

      Volume: 4 Pages: 21-24

    • NAID

      130003371115

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Presentation] dqds 法および mdLVs 法の新しい実装法について2016

    • Author(s)
      木村欣司, 中村佳正
    • Organizer
      日本応用数理学会研究部会連合発表会
    • Place of Presentation
      神戸学院大学(兵庫県・神戸市)
    • Year and Date
      2016-03-04
    • Related Report
      2015 Annual Research Report
  • [Presentation] クラスタ行列に対する直交QD法の特異値分解精度を改善する停止条件について2016

    • Author(s)
      荒木翔, 木村欣司, 中村佳正
    • Organizer
      日本応用数理学会研究部会連合発表会
    • Place of Presentation
      神戸学院大学(兵庫県・神戸市)
    • Year and Date
      2016-03-04
    • Related Report
      2015 Annual Research Report
  • [Presentation] Thick-Restart GKL法の新しいリスタートの方法について2016

    • Author(s)
      石田遊也,木村欣司,中村佳正
    • Organizer
      日本応用数理学会研究部会連合発表会
    • Place of Presentation
      神戸学院大学(兵庫県・神戸市)
    • Year and Date
      2016-03-04
    • Related Report
      2015 Annual Research Report
  • [Presentation] Bisection and inverse iteration algorithms for computing eigenpair subsets of symmetric band matrices2015

    • Author(s)
      Hiroyuki Ishigami, Kinji Kimura, Yoshimasa Nakamura
    • Organizer
      International Workshop on Eigenvalue Problems: Algorithms; Software and Applications, in Petascale Computing (EPASA2015)
    • Place of Presentation
      Tsukuba International Congress Center(茨城県・つくば市)
    • Year and Date
      2015-09-14
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 直交 QD 法 (random-time Toda molecule equation) の実装の詳細につ いて2015

    • Author(s)
      木村欣司, 石上裕之, 中村佳正
    • Organizer
      日本応用数理学会年会
    • Place of Presentation
      金沢大学(石川県・金沢市)
    • Year and Date
      2015-09-09
    • Related Report
      2015 Annual Research Report
  • [Presentation] Xeon Phiにおける並列2分法による固有値計算の性能評価2015

    • Author(s)
      木村欣司, 石上裕之, 中村佳正
    • Organizer
      情報処理学会 2015年並列/分散/協調処理に関するサマー・ワークショップ (SWoPP2015)
    • Place of Presentation
      別府ビーコンプラザ(大分県・別府市)
    • Year and Date
      2015-08-04
    • Related Report
      2015 Annual Research Report
  • [Presentation] Performance evaluation of Golub-Kahan-Lanczos algorithm with reorthogonalization by classical Gram-Schmidt algorithm and OpenMP2015

    • Author(s)
      Masami Takata, Hiroyuki Ishigami, Kinji Kimura, Yuki Fujii, Hiroki Tanaka, Yoshimasa Nakamura
    • Organizer
      The 2015 International Conference on Parallel and Distributed Processing Techniques and Applications(PDPTA2015)
    • Place of Presentation
      Las Vegas, Monte Carlo Resort(Las Vegas, USA)
    • Year and Date
      2015-07-27
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Xeon Phi における部分固有対計算の高速化に向けて2015

    • Author(s)
      石上裕之, 木村欣司, 中村佳正
    • Organizer
      日本応用数理学会研究部会連合発表会
    • Place of Presentation
      明治大学
    • Year and Date
      2015-03-06 – 2015-03-07
    • Related Report
      2014 Annual Research Report
  • [Presentation] 直交QD アルゴリズムによる高精度特異値分解について2015

    • Author(s)
      田中博基, 木村欣司, 石上裕之, 中村佳正
    • Organizer
      日本応用数理学会研究部会連合発表会
    • Place of Presentation
      明治大学
    • Year and Date
      2015-03-06
    • Related Report
      2014 Annual Research Report
  • [Presentation] 部分固有対計算ソフトウェアARPACK の改良について2014

    • Author(s)
      藤井祐貴, 石上裕之, 木村欣司, 中村佳正
    • 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
      東京大学工学部
    • Year and Date
      2014-12-25
    • Related Report
      2014 Annual Research Report
  • [Presentation] 高精度特異値分解のための直交QD アルゴリズムの改良2014

    • Author(s)
      田中博基, 石上裕之, 木村欣司, 中村佳正
    • 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
      東京大学工学部
    • Year and Date
      2014-12-25
    • Related Report
      2014 Annual Research Report
  • [Presentation] Accelerating the numerical computation of positive roots of polynomials using improved bounds2014

    • Author(s)
      Kinji Kimura, Takuto Akiyama, Hiroyuki Ishigami, Masami Takata, Yoshimasa Nakamura
    • Organizer
      The 2014 International Conference on Parallel and Distributed Processing Techniques and Applications(PDPTA2014),
    • Place of Presentation
      Las Vegas, USA
    • Year and Date
      2014-07-21 – 2014-07-24
    • Related Report
      2014 Annual Research Report
  • [Presentation] Implementation of the orthogonal QD-algorithm for performing singular value decomposition with high accuracy2014

    • Author(s)
      Hiroki Tanaka, Hiroyuki Ishigami, Kinji Kimura, Yoshimasa Nakamura
    • Organizer
      8th International Workshop on Parallel Matrix Algorithms and Applications (PMAA2014)
    • Place of Presentation
      Lugano, Switzerland
    • Year and Date
      2014-07-02 – 2014-07-04
    • Related Report
      2014 Annual Research Report
  • [Presentation] Speed-up of reorthogonalized block Golub-Kahan-Lanczos algorithm for preprocessing2014

    • Author(s)
      Yuki Fujii, Hiroyuki Ishigami, Kinji Kimura, Yoshimasa Nakamura
    • Organizer
      8th International Workshop on Parallel Matrix Algorithms and Applications (PMAA2014)
    • Place of Presentation
      Lugano, Switzerland
    • Year and Date
      2014-07-02 – 2014-07-04
    • Related Report
      2014 Annual Research Report
  • [Presentation] 高精度特異値分解を表現するoqds 法のシフト戦略について2014

    • Author(s)
      田中博基, 木村欣司, 中村佳正
    • Organizer
      日本応用数理学会研究部会連合発表会
    • Place of Presentation
      京都大学
    • Related Report
      2013 Annual Research Report
  • [Presentation] 再直交化付きブロック逆反復法による固有ベクトルの並列計算2014

    • Author(s)
      石上裕之,木村欣司,中村佳正
    • Organizer
      情報処理学会2014 年ハイパフォーマンスコンピューティングと計算科学シンポジウム
    • Place of Presentation
      一橋講堂
    • Related Report
      2013 Annual Research Report
  • [Presentation] 下3 重対角行列向けoqds 法について2013

    • Author(s)
      荒木翔,田中博基,木村欣司,中村佳正
    • 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
    • Place of Presentation
      東京大学
    • Related Report
      2013 Annual Research Report
  • [Presentation] Reorthogonalized-Golub-Kahan-Lanczos 法と拡大行列に対するReorthogonalized-Lanczos 法の比較について2013

    • Author(s)
      藤井祐貴, 石上裕之, 木村欣司, 中村佳正
    • Organizer
      日本応用数理学会年会
    • Place of Presentation
      アクロス福岡
    • Related Report
      2013 Annual Research Report
  • [Presentation] 新シフト戦略によるoqds 法の反復回数の削減と高精度特異値分解への応用2013

    • Author(s)
      田中博基, 山下巧, 木村欣司, 中村佳正
    • Organizer
      日本応用数理学会年会
    • Place of Presentation
      アクロス福岡
    • Related Report
      2013 Annual Research Report
  • [Presentation] 逆反復に基づく並列固有ベクトル計算のブロックCGS2アルゴリズムの適用による高速化2013

    • Author(s)
      石上裕之, 木村欣司, 中村佳正
    • Organizer
      応用数理学会研究部会連合発表会
    • Place of Presentation
      東洋大学
    • Related Report
      2012 Annual Research Report
  • [Presentation] Accelerating the Reorthogonali zat i on on Singular Vectors with a Multi-Core Processor2012

    • Author(s)
      Hiroki Toyokawa, Hiroyuki Ishigami, Kinji Kimura, Masami Takata, and Yoshimasa Nakamura
    • Organizer
      The Seventh International Workshop on Automatic Performance Tuning (iWAPT2012)
    • Place of Presentation
      RIKEN Advanced Institute for Computational Science, Kobe
    • Year and Date
      2012-07-17
    • Related Report
      2012 Annual Research Report
  • [Presentation] Performance Evaluation of Some Inverse Iteration Algorithms on PowerXCellTM 8i Processor2012

    • Author(s)
      Masarai Takata, Hiroyuki Ishigami, Kinji Kimura, and Yoshimasa Nakamura
    • Organizer
      The 2012 International Conference on Parallel and Distributed Processing Techniques and Applications (PDPTA2012)
    • Place of Presentation
      Monte Carlo Resort, Las Vegas
    • Related Report
      2012 Annual Research Report
  • [Presentation] compact WY直交化法の計算量を削減する実装について2012

    • Author(s)
      石上裕之, 木村欣司, 中村佳正
    • Organizer
      日本応用数理学会年会
    • Place of Presentation
      稚内全日空ホテル
    • Related Report
      2012 Annual Research Report
  • [Presentation] GPUによる逆反復法の高速化について2012

    • Author(s)
      秋山拓斗, 石上裕之, 木村欣司, 中村佳正
    • Organizer
      日本応用数理学会年会
    • Place of Presentation
      稚内全日空ホテル
    • Related Report
      2012 Annual Research Report
  • [Remarks] Singular value decomposition code DBDSLV

    • URL

      http://www-is.amp.i.kyoto-u.ac.jp/lab/en/isvd/

    • Related Report
      2015 Annual Research Report
  • [Remarks] 倍精度2 重対角行列特異値分解コードDBDSLVを含む密行列の特異値分解コードの公開

    • URL

      http://www-is.amp.i.kyoto-u.ac.jp/svd/index.html

    • Related Report
      2013 Annual Research Report
  • [Remarks]

    • URL

      http://www.amp.i.kyoto-u.ac.jp/

    • Related Report
      2012 Annual Research Report

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Published: 2012-04-24   Modified: 2019-07-29  

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