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ALGEBRAIC ALGORITHMS AND NUMERICAL ALGORITHMS

Research Project

Project/Area Number 10680357
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field 計算機科学
Research InstitutionYAMAGUCHI UNIVERSITY

Principal Investigator

LI Lei  YAMAGUCHI UNIVERSITY FACULTY OF SCIENCE ASSOCIATE PROFESSOR, 理学部, 助教授 (50244893)

Project Period (FY) 1998 – 2000
Project Status Completed (Fiscal Year 2000)
Budget Amount *help
¥2,900,000 (Direct Cost: ¥2,900,000)
Fiscal Year 2000: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 1999: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 1998: ¥1,400,000 (Direct Cost: ¥1,400,000)
KeywordsALGORITHM / FAST / PARALLEL / COMPUTATIONAL COMPLEXITY / VANDERMONDE / P-MATRIX / H-MATRIX / LCP / P-Matrices / Matrix / 行列 / 収束性 / 計算複雑さ / H行列 / 並列処理
Research Abstract

In this project, we have researched design and analysis of algebraic algorithms and numerical algorithms for scientific computation. Connection of the algebraic and numerical algorithms, and the upper bounds of some computational complexities became clear. We have got the following research results in collaboration with some overseas researchers. Put emphasis on H-matrices, we found many practical distinguishing conditions for convergence of the algorithms and stabilities of control systems, and proposed a fast algorithm for finding the trigonometric sums which are often appeared in signal processing. An approximate parallel solution of integral equation for radiative heat exchange and a parallel algorithm for solving the implicit defusion deference equations was proposed separately. The time complexity for testing whether an n-by-n real matrix is a P-matrix is reduced from O(2^n n^3) to O(2^n) by applying recursively a criterion for P-matrices based on Schur complementation. A Matlab program implementing the associated algorithm is provided. We also presented some new fast algorithms for solving an norder Vandermonde linear system of equations, and Vandermonde determinants. The arithmetic operational complexity of these algorithms will be not more than O(n logn^2). This research also proposed an O(n^3) recursive algorithm for solving the LCP (A, q) with A is an M-matrix.

Report

(4 results)
  • 2000 Annual Research Report   Final Research Report Summary
  • 1999 Annual Research Report
  • 1998 Annual Research Report
  • Research Products

    (37 results)

All Other

All Publications (37 results)

  • [Publications] L.Li,H.Niki,M.Sasanabe: "A Nonparameter Criterion for GDDM"Inter.J.of Computer Mathematics. 71. 267-275 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] B.Li,L.Li,M.Harada 等: "An Iterative Criterion for H-matrices"Linear Algebra and Its Appl.,. 271. 179-190 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] L.Li,B.Zhang: "A Parallel Algorithm for Solving the Implicit DDE"Inter.J.of Computer Mathematics. 67. 431-440 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] L.Li,T.Yahagi: "Fast Algorithms for Finding the Trigonometric Sums"J.of Signal Processing. 2. 167-171 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] L.Li: "On the Arithmetic Operational Complexity"Japan J.of Indus & Appl., Math,. 17. 15-18 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] L.Li,T.Nakamura: "Fast Parallel Algorithms for Vandermonde Determinants"Inter.J.of Computer Math.. 73. 479-486 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] 谷萩,李 他: "高速アルゴリズムと並列信号処理"コロナ社. 254 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] 北京市青年連合会: "現代科学知識熱点問題450例"科学普及出版社. 480 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] L.Li, H.Niki, M.Sasanabe: "A Nonparameter Criterion for GDDM"Inter.J.of Computer Math.. 71. 267-275 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] B.Li, L.Li, M.Harada, etc: "An Iterative Criterion for H-matrices"Linear Algebra and Its Appl.. 271. 179-190 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] L.Li, B.Zhang: "A Parallel Algorithm for Solving the Implicit Defusion Deference Equations"Inter.J.of Computer Math.. 67. 435-440 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] L.Li, T,Yahagi: "Fast Algorithms for Finding the Trigonometric Sums"Journal of Signal Processing. 2. 167-171 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] L.Li: "On the Arithmetic Operational Complexity"Japan J.of Indus. & Appl.Math.. 17. 15-18 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] L.Li, T.Nakamura: "Fast Parallel Algorithms for Vandermonde Determinants"Inter.J.of Computer Math.. 73. 479-486 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] H.Yahagi, L.Li etc: "Fast Algorithms and Parallel Signal Processing"Korona Publishing. 1-254 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Beijing Youth Union: "450 Keywords in Modern Sciences and Technologies"Science Spread Publishing. 1-480 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Lei Li: "On the Arithmetic Operational Complexity for Solving Vandermonde Linear Equations"Japan J. of Indus. & Appl.Math.. 17・1. 15-18 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Lei Li,Tadao Nakamura: "Fast Parallel Algorithms for Vandermonde Determinants"Inter.J.Computer Math.. 73・3. 479-486 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] M.J.Tsatsomeros,Lei Li: "A Recursive Test for P-Matrices"BIT. 40・2. 410-414 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Lei Li : "Distinguishing the H-Matrix"Information. 3・2. 167-176 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Lei Li,Y.Okubo : "A Recursive Algorithm for LCP with an M-matrix"AMS-HKMS Meeting 2000. Dec.13-16. (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] 谷萩隆嗣 他: "高速アルゴリズムと並列信号処理"コロナ社. 254 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] M.J.Tsatsomeros,Lei.Li: "A Recursive Test for P-Matrices"BIT. (掲載予定). (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] Lei Li: "On the arithmetic Operational complexity"The Japan J. of Indus and Appl. Math. 17・1. 15-18 (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] Lei Li,T.Nakamura: "Fast Parallel Algorithms for Vandermonde DET"Inter.J.of computer Math.. 73・4. 不-明 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Lei Li: "On Convergence of the Extrapolate Relaxation"Chinese J. of Engineering Mathematics. (掲載予定). (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] Lei Li, H. Niki, M. Sasanabe: "A Nonparameter Criterion for GDDM"Inter.J of Computer Math.. 71・. 267-275 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Y.Huang, A.J.Wathen, Lei Li: "An Iterative Mathod for Skew-Symmetric Systems"Information. 2・2. 147-153 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 谷萩隆嗣、李磊: "高速アルゴリズムと並列信号処理"コロナ社. 220 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 北京青年連合会(共著): "現代科学キーワード500例"北京科学技術出版社. 385 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Y.Ren,L.Li: "An Approximate Solution of Integral Equation" Information. 1・2. 23-32 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] L.Li,H.Niki,M.Sasanabe,: "A Nonparameter Criterion for GDDM" Inter.J.of Computer Mathematics. 72. 発表予定 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 藤野清次等: "一般化優対角行列判別法の流れ解析への応用と評価" Information. 1・2. 75-84 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] L.Li,T.Yahagi: "Fast Algorithms for Finding the Trigonometric Sums" J.of Signal Processing. 2・2. 167-171 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] L.Li,B.Zhang: "A Parallel Algorithm for Solving the Implicit Diffusion" Inter.J.of Computer Mathematics. 67. 435-440 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] B.Li,L : Li,等: "An Iterative Criterion for H-Matrices" Linear Algebra and Its Appl.271. 179-190 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] S.N.Atluri 等(分担): "Modeling and Simulation Based Engineering" Tech.Science Press,USA(2巻), 700 (1998)

    • Related Report
      1998 Annual Research Report

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Published: 1998-04-01   Modified: 2016-04-21  

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