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Research and Development of User-Friendly Mathematical Software.

Research Project

Project/Area Number 06650075
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Engineering fundamentals
Research InstitutionNagoya University

Principal Investigator

TORII Tatsuo  Graduate School of Engineering Nagoya University Professor, 工学部, 教授 (10029069)

Co-Investigator(Kenkyū-buntansha) HASEGAWA Takemitsu  Fukui University, Faculty of Engineering Professor, 工学部, 教授 (70023314)
MITSUI Taketomo  Graduate School of Human Informatics, Nagoya University Professor, 人間情報学研究科, 教授 (50027380)
SAITO Satoshi  Graduate School of Engineering Nagoya University Research Assistan, 工学部, 助手 (70252252)
ZHANG Shao-Liang  Institute of Information Sciences and Electronics, University of Tsukuba, Assist, 電子・情報工学系, 講師 (20252273)
SUGIURA Hiroshi  Graduate School of Engineering Nagoya University Associate Professor, 工学部, 助教授 (60154465)
Project Period (FY) 1994 – 1996
Project Status Completed (Fiscal Year 1996)
Budget Amount *help
¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 1996: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 1995: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 1994: ¥700,000 (Direct Cost: ¥700,000)
KeywordsSimultaneous Method for Algebraic Equations / Two-Step Runge-Kutta Methods / Stochastic Differential Equations / Delay-Differential Equations / KP Equation / Hilbert Transform / GPBi-CG method / Mathematical Notation Understanding / 全根同時反復法 / 確率微分方程式の数値解法 / ROW型公式 / 差分微分方程式の数値解法 / 振動関数の無限区間積分 / 積型反復法 / 多項式剰余列 / Givens回転 / 非斉次2階差分方程式 / 非優越解 / 優良格子点法 / 積型反復公式 / Two-Step Runge-Kutta法 / Collocation Runge-Kutta法 / ユークリッドの互助法 / 数学ソフトウェア / 数値ヒルベルト変換 / アダマ-ル変換 / 有理関数近似 / 非線型方程式 / 多重積分 / 大規模線型方程式
Research Abstract

To construct user-friendly mathematical software, we studied on numerical analysis and human-interface for mathematical computation. In the field of numerical analysis, we developed new algorithms for fundamenetal computational task, i.e., algebraic equations (T.Torii & H.Sugiura with collaborators), ordinary differential equations (T.Mitsui & H.Sugiura with collaborators), Stochastic Differential Equations (T.Mitsui & H.Sugiura with collaborators), Delay-Differential Equations (by T.Mitsui with collaborators), Soliton Equations (T.Mitsui with collaborators), Numerical Integration (T.Hasegawa, T.Torii & H.Sugiura with collaborators), Linear Equations (S.-L.Zhang, T.Mitsui, T.Hasegawa, T.Torii & H.Sugiura with collaborators), polynomial remainder sequence for rational apploximation of function (T.Torii & H.Sugiura with collaborators).
In the field of human-interface for mathematical computation, we studied mathematical notation understanding (T.Torii & H.Sugiura with collaborators) and curve-surface generation (T.Torii & H.Sugiura with collaborators). On the research of the first theme, we achieved fundamental results of the input and parsing of mathematical notation for improving the environment of mathematical computation. Using our result, we can construct environment of programing with natural mathematical notations. Our result also gives a foundation for constructing a data-base which contains data written in mathematical notations, for example, a table of mathematical formulae. On the second theme, we studied generation of curve and surface with constraints, and propose several new algorithms. It is natural in real geometric design that curves or surfaces must satisfy some constraints, for example, positivity, monotonicity or convexity.

Report

(4 results)
  • 1996 Annual Research Report   Final Research Report Summary
  • 1995 Annual Research Report
  • 1994 Annual Research Report
  • Research Products

    (25 results)

All Other

All Publications (25 results)

  • [Publications] C. Carstensen & T. Sakurai: "Simultaneous tactorization of a Polynomial by rational Apploximation" J. Compt. Appl. Math.61. 165-178 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] N. H. Cong, T. Mitsui: "Aclass of explicit Parallal two-seep Runge-Kutta Methods" Japan Journal of Industrial and Applied Math.(to-appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Y. Komori, H. Sugiura & T. Mitsui: "Rooted Tree Analysis of the order conditions of ROW-type scheme for stochastic pitterential Eguations" BIT. 31. 43-66 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] S. -L. Zhang: "GPBi-CG : Generalized Product-Type Methods based on Bi-CG for solving nonsymmetric linear systems" SIAM J. Sci. Comput. 18 (to-appear). (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] T. Hasegawa & T. Torii: "Hilbert and Hadamard Trans forms by Generalized chebyshev Expansion" J. Compt. and Appl. Math.51. 71-83 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Y. Zhao, H. Sugiura, T. Sakurai & T. Torii: "A knowledge-Based Method for Mathe matical Notation Understarding" Trans. Infomation Processing Society of Japan. 35. 2366-2381 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] T.Sakurai & M.S.Petkovi'C: "On Some Simultaneous Methods Based on Weierstrass' Correction" J.Compt.Appl.Math.72. 275-291 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] Y.Komori,T.Mitsui & H.Sugiura: "Rooted Tree Analysis of the Order Conditions of ROW-Type Scheme for Stochastic Differential Equations" BIT. 37・1. 43-66 (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] G.-D.Hu & T.Mitsui: "Stability of linear Delay differential systems with Matrices Heving Common Eigenrectors" Japan J.Industr.Appl.Math.13. 487-494 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] T.Hasegawa & A.Sidi: "An Automatic Integration Procedure for Intinite Range Integrals Involving Oscillatory kernels" Numerical Algorithms. 13・1. 1-19 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] 阿部邦美,張紹良,三井斌友: "MRTR法:CG型の三項漸化式に基づく非対称行列のための反復解法" 日本応用数理学会論文誌. 7(印刷中). (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] 大迫尚行,杉浦洋,鳥居達生: "Givens回転による多項式剰余列の拡張算法" 情報処理学会論文誌. 38・1. 158-160 (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] Takemitsu Hasegawa and Tatsuo Torii: "An Algorithm for Nondominant Solution of Linear Second-Order Inhomogeneous Difference Equations" Math.Comp.64-211. 1199-1234 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] 大迫尚行,鳥居達生,杉浦洋,桜井鉄也: "多項式剰余列の安定な生成法" 日本応用数理学会論文誌. 5-3. 241-255 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] Hiroshi Sugiura: "3,4,5,6 Dimentional Good daftice Points Formulae" Advances in Numerical Mathematics(decture Notes in Numerical and Applied Analysis). 14. 181-197 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] Shao-Liang Zhang: "Some Product-Type Kylor Subspace Methods for Solving Nongymmetric Linear Systems." Advances in Numerical Mathematics(Lecture Notes in Numerical and Applied Analysis). 14. 275-278 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] T.Mitsui & H.Sugiura: "A Series of Collocation Runge-Kutta Methods" Numerical Analysis of Ordinary Differential Equations and Its Applications.1. 15-28 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] Nguyen huu Cong & Taketomo Mitsui: "Collocation-Based Two-Step Runge-Kutta Methods" Japan Journal of Industrial and Applied Math.3-1. 171-183 (1996)

    • Related Report
      1995 Annual Research Report
  • [Publications] 鳥居 達生: "Hilbert and Hadmard Transforms by Generalized Chebyshev Expansion" J. of Computional and Applied Mathematics. 51-1. 71-83 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] 杉浦 洋: "Wegmann法に基づく数値等角写像の自動化について" 情報処理学会論文誌. 35-2. 309-312 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] 杉浦 洋: "Durand-kerner型補助関数を用いた非線型方程式の多段反復法" 日本応用数理学会論文誌. 4-2. 67-80 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] 三井 斌友: "確率微分方程式の数値スキームの誤差における統計的部分" 日本応用数理学会論文誌. 4-2. 127-139 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] 趙 燕結: "A Knowledge-Based Method for Mathematical Notations Understanding" 情報処理学会論文誌. 35-11. 2366-2381 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] 細田 陽介: "悪条件線型方程式に対する一つの直接解放" 日本応用数理学会論文誌. 4-4. 287-298 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] 島内 剛一: "アルゴリズム辞典" 共立出版株式会社, 951 (1994)

    • Related Report
      1994 Annual Research Report

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Published: 1994-04-01   Modified: 2016-04-21  

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