1997 Fiscal Year Final Research Report Summary
Research on High Dimension Problems in Numerical Analysis.
| Project/Area Number |
07805009
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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 |
Engineering fundamentals
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| Research Institution | Nagoya University |
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Principal Investigator |
SUGIURA Hiroshi Nagoya University, Graduate School of Engineering Associate Professor, 工学研究科, 助教授 (60154465)
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| Co-Investigator(Kenkyū-buntansha) |
MITSUI Taketomo Nagoya University, Graduate School of Human Informatics Professor, 人間情報学研究科, 教授 (50027380)
ZHANG Shao-Liang University of Tsukuba, Institute of Information Sciences and Electronics, Assist, 電子・情報工学系, 講師 (20252273)
TORII Tatsuo Nagoya University, Graduate School of Engineering Professor, 工学研究科, 教授 (10029069)
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| Project Period (FY) |
1995 – 1997
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| Keywords | Good Lattice Points Methods / Sparse Grid Methods / Product-type Krylov-Subspace Methods / Two-Step Runge-Kutta Methods / Stochastic Differential Equations / ROW-Type Scheme / Grobner Basis / Characteristic Curve |
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| Research Abstract |
We investigated fast numerical algorithms for solving high dimensional problems and efficient implementation for fast computers with parallel or vector architecture.
On the field of algebraic calculation, we found new algorithms for numerical factorization of polynomials and an algorithm for sequence of polynomial remainders. And we also investigate stable numerical algorithms for Grobner basis and basis of quotient rings of polynomials.
On the field of ordinary differential equations, we proposed new scheme of two-step Runge-Kutta methods suitable for parallel computing and investigated characteristic curve methods solving convection and diffusion problems as an application of parallel ODE solvers.
On stochastic differential equations, we found the order conditions of ROW-type scheme by rooted tree analysis. We also proposed new stability criteria for numerical scheme.
On delay-differential equations, we investigate the stability of linear systems and proposed several methods for determine stability of linear systems and numerical solver.
On soliton equations, we found new algorithm for KP equations which represents a two dimensional soliton.
On high dimensional integration, we proposed high precision good lattice points methods. We also developed a new method named sparse grid method.
On high dimensional linear equations, we proposed GPBi-CG,which is a generalized product-type methods based on Bi-CG for solving nonsymmetric linear systems. We also proposed rotated alternative LU decomposition which is suitable for vector architecture.
For visualization of high dimensional mathematical problems, we investigate the generation of sprine curves with several constraints, i.e., positivity, monotonisity and convexity.
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Research Products
(23 results)
