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2009 Fiscal Year Final Research Report

Study of Algorithms and Applications of Approximate Algebra

Research Project

  • PDF
Project/Area Number 19300001
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Fundamental theory of informatics
Research InstitutionUniversity of Tsukuba

Principal Investigator

SASAKI Tateaki  University of Tsukuba, 名誉教授 (80087436)

Co-Investigator(Kenkyū-buntansha) SAKURAI Tetsuya  筑波大学, 大学院・システム情報工学研究科, 教授 (60187086)
TERUI Akira  筑波大学, 大学院・数理物質科学研究科, 助教 (80323260)
KAI Hiroshi  愛媛大学, 大学院・理工学研究科, 准教授 (10274341)
KAKO Fujio  奈良女子大学, 理学部, 教授 (90152610)
FUKUI Tetsuo  武庫川女子大学, 生活環境学部, 教授 (70218890)
Project Period (FY) 2007 – 2009
Keywordsアルゴリズム理論 / 数式処理 / 数値数式融合算法 / 数値解析
Research Abstract

For computing Groebner bases with inaccurate input coefficients, we clarified origins of instability and proposed a stable method "high-precision method with effective floating-point numbers". As for series expansion of multivariate algebraic function at singular point, we devised a method which gives the series in a compact form, derived a simple expansion formula, and clarified many properties of convergence and many-valuedness. We devised a method which computes only eigenvalues located in a specified domain, and applied the method to large-scale chemical computations successfully. We made Japanese algebra system GAL run on C.

  • Research Products

    (23 results)

All 2010 2009 2008 2007 Other

All Journal Article (23 results) (of which Peer Reviewed: 23 results)

  • [Journal Article] A filter diagonalization for generalized eigenvalue problems based on the Sakurai-Sugiura projection method2010

    • Author(s)
      T. Ikegami, T. Sakurai, U. Nagashima
    • Journal Title

      J.Comput, Appl.Math.

      Pages: 1927-1936

    • Peer Reviewed
  • [Journal Article] A practical method for floating-point Groebner basis computation2009

    • Author(s)
      Tateaki Sasaki
    • Journal Title

      Proc.of Joint Conference of ASCM 2009 and MACIS

      Pages: 167-176

    • Peer Reviewed
  • [Journal Article] Series expansion of multivariate algebraic functions at singular point-nonmonic case-2009

    • Author(s)
      T. Sasaki, D. Inaba
    • Journal Title

      Proc.of Joint Conference of ASCM 2009 and MACIS

      Pages: 177-186

    • Peer Reviewed
  • [Journal Article] Convergence and many-valuedness of Hensel series near the expansion point2009

    • Author(s)
      T. Sasaki, D. Inaba
    • Journal Title

      Proc.of SNC' 09

      Pages: 159-167

    • Peer Reviewed
  • [Journal Article] Approximate factorization of polynomials over Z2009

    • Author(s)
      T. Sasaki, Y. Ookura
    • Journal Title

      Proc.of SNC' 09

      Pages: 169-176

    • Peer Reviewed
  • [Journal Article] Computing clustered close-roots of univariate polynomials2009

    • Author(s)
      T. Sasaki, A. Terui
    • Journal Title

      SNC' 09

      Pages: 177-184

    • Peer Reviewed
  • [Journal Article] Error analysis for a matrix pencil of Hankel matrices with perturbed complex moments2009

    • Author(s)
      T. Sakurai, ほか3名
    • Journal Title

      JSIAM Letters

      Pages: 76-79

    • Peer Reviewed
  • [Journal Article] A method for finding zeros of polynomial equations using a contour integral based eigensolver2009

    • Author(s)
      T. Sakurai, ほか4名
    • Journal Title

      Proc.of SNC' 09

      Pages: 143-147

    • Peer Reviewed
  • [Journal Article] A numerical method for nonlinear eigenvalue problems using contour integrals2009

    • Author(s)
      J. Asakura, T. Sakurai, ほか3名
    • Journal Title

      JSIAM Letters

      Pages: 52-55

    • Peer Reviewed
  • [Journal Article] A new block Krylov subspace method for computing high accuracy solutions2009

    • Author(s)
      H. Tadano, T. Sakurai, Y. Kuramashi
    • Journal Title

      JSIAM Letters Vol. 1

      Pages: 44-47

    • Peer Reviewed
  • [Journal Article] Floating-point Groebner base computation with illconditionedness estimation2008

    • Author(s)
      T. Sasaki, F. Kako
    • Journal Title

      LNAI Vol. 5081

      Pages: 278-292

    • Peer Reviewed
  • [Journal Article] 精度混合型 Krylov 部分空間反復法における疎行列ベクトル積の Cell Be 上での実装と性能評価2008

    • Author(s)
      山崎育朗, 櫻井鉄也, ほか3名
    • Journal Title

      情報処理学会論文誌コンピューティングシステム 1巻

      Pages: 51-60

    • Peer Reviewed
  • [Journal Article] Cutoff を2重に用いた前処理の性能評価2008

    • Author(s)
      山崎育朗, 櫻井鉄也, ほか4名
    • Journal Title

      日本応用数理学会論文誌 18巻

      Pages: 135-153

    • Peer Reviewed
  • [Journal Article] A MathML content markup editor on the xfy2008

    • Author(s)
      T. Kawata, H. Kai, Y. Tamura
    • Journal Title

      Electric Proc.Of ACA2008

      Pages: 1-5

    • Peer Reviewed
  • [Journal Article] Computing floating-point Groebner bases stably2007

    • Author(s)
      T. Sasaki, F. Kako
    • Journal Title

      Proc.SNC'07

      Pages: 180-189

    • Peer Reviewed
  • [Journal Article] A numerical study of extended Hensel series2007

    • Author(s)
      D. Inaba, T. Sasaki
    • Journal Title

      Proc.SNC'07

      Pages: 103-109

    • Peer Reviewed
  • [Journal Article] Computing approximate GCDs in ill-conditioned cases2007

    • Author(s)
      M. Sanuki, T. Sasaki
    • Journal Title

      Proc.SNC'07

      Pages: 161-169

    • Peer Reviewed
  • [Journal Article] Tighter bounds of errors of numerical roots2007

    • Author(s)
      T. Sasaki
    • Journal Title

      JJIAM Vol. 24

      Pages: 219-226

    • Peer Reviewed
  • [Journal Article] A verified method for bounding clusters of zeros of analytic functions2007

    • Author(s)
      X. Niu, T. Sakurai, H. Sugiura
    • Journal Title

      J.Comput.Appl.Math. Vol. 199

      Pages: 263-27

    • Peer Reviewed
  • [Journal Article] AMLS法による固有値分布の推定2007

    • Author(s)
      先崎健太, 多田野寛人, 櫻井鉄也
    • Journal Title

      日本応用数理学会論文誌 17巻

      Pages: 511-521

    • Peer Reviewed
  • [Journal Article] 近似係数行列に対する疎行列用直接解法を用いた前処理2007

    • Author(s)
      岡田真幸, 櫻井鉄也, 寺西慶太
    • Journal Title

      日本応用数理学会論文誌 17巻

      Pages: 319-329

    • Peer Reviewed
  • [Journal Article] On single precision preconditioners for Krylov subspace iterative methods2007

    • Author(s)
      H. Tadano, T. Sakurai
    • Journal Title

      LNCS Vol. 4818

      Pages: 708-715

    • Peer Reviewed
  • [Journal Article] A numerical method for polynomial eigenvalue problems using contour integral

    • Author(s)
      J. Asakura, T.Sakurai, ほか3名
    • Journal Title

      Japan J.Indust.Appl.Math.

    • Peer Reviewed

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Published: 2011-06-18   Modified: 2016-04-21  

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