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| New method in solving linear system of equations |
| Revised:June 12, 2002 |
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| DOI：10.7511/jslx20036135 |
| KeyWord:general coefficient matrix,symmetric positive matrix,good-conditioned linear system of equations,ill-conditioned linear system of equations,variational problem,half-division optimization method |
| Shi Wenpu~1 Liu Yingxi~2 Chu Jinglian~3 Guo Shuhong~3 |
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| Abstract: |
| At the two sides of a system of linear equations, simultaneously left multiplying the conjugate matrix corresponding its coefficient matrix, the general coefficient matrix is changed into a symmetric positive one. Based on the variational principle, the solving problem for the original group of linear equation is transformed into an equivalent no constrained optimization programming. Then a half-division optimization method can be used to solve the problem. The results of the given examples prove that the method is effective for good-conditioned or ill-conditioned group of linear equations. Compared with the steepest descent method, Newton method and conjugate gradient method etc. show that the method provided has the following characteristics, such as wide suiting range, high convergence rate, high convergence precision, no beginning iteration point, simple algorithm, easy programming, strong ill conditioned-resistant. At last, the shortcomings of the method are also discussed. |
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