2005 Fiscal Year Final Research Report Summary
The synthetic research for the basic iterative method for the non-diagonal dominant matrix.
Grant-in-Aid for Scientific Research (C)
|Allocation Type||Single-year Grants |
General mathematics (including Probability theory/Statistical mathematics)
|Research Institution||Okayama University of Science |
NIKI Hiroshi Okayama University of Science, Professor -> 岡山理科大学, 客員教授(常勤) (30068879)
AWAMI Hideon Okayama University of Science, Informatics, Professor, 総合情報学部, 教授 (70098581)
HAMAYA Yoshihiro Okayama University of Science, Informatics, Professor, 総合情報学部, 教授 (40228549)
CHEN Xiaojun Hirosaki University, Science and Technology, Professor, 理工学部, 教授 (70304251)
ABE Kuniyoshi Gifu Shoutoku University, Economics and Information, Assistant professor, 経済情報学部, 助教授 (10311086)
KOHNO Toshiyuki Okayama University of Science, Infomatics, Assistant, 総合情報学部, 助手 (90309534)
|Project Period (FY)
2003 – 2005
|Keywords||accuracy / H-matrix / preconditioning / the iterative method / finite difference / the CG method / Kryllov su space method / NCP function|
(1)Development of the new preconditioning matrix
We developed the new preconditioning matrix. Using the new preconditioning matrix can be accelerate of convergence of the classical Gauss-Seidel method. Moreover, it is possible to solve a non-diagonal dominant matrix which is impossible to apply the iterative method. On the other hand, Kohno developed other type's preconditioning matrix and obtained many effective results. The proposed method is excellent in iterative numbers and CPU time as compared with the ICCG method.
(2)Development of criterion of the H-matrix.
The H-matrix is very important for the solution of linear systems of algebraic equations by the iterative methods. But there is not criterion for the H-matrix. We developed the iterative criterion as new criterion. This method is our completely original. However, many iteration numbers are needed in judge to all H-matrix. In order to conquer this fault, we discovered new iterative criterion
(3)We give new error bounds for the linear complementarity problem where the involved matrix is a P-matrix. Computation of rigorous error bounds can be turned into P-matrix linear interval system. Moreover, for the involved matrix being an H-matrix with positive diagonals, an error bound can be found by solving a linear system of equations which is sharper than the Mathias-Pang error bound.
Research Products (16 results)