2000 Fiscal Year Final Research Report Summary
ALGEBRAIC ALGORITHMS AND NUMERICAL ALGORITHMS
| Project/Area Number |
10680357
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
計算機科学
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| Research Institution | YAMAGUCHI UNIVERSITY |
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Principal Investigator |
LI Lei YAMAGUCHI UNIVERSITY FACULTY OF SCIENCE ASSOCIATE PROFESSOR, 理学部, 助教授 (50244893)
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| Project Period (FY) |
1998 – 2000
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| Keywords | ALGORITHM / FAST / PARALLEL / COMPUTATIONAL COMPLEXITY / VANDERMONDE / P-MATRIX / H-MATRIX / LCP |
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| 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.
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