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| Precise integration method for solving ill-conditioned algebraic equations |
| Received:December 09, 2009 Revised:September 02, 2010 |
| View Full Text View/Add Comment Download reader |
| DOI：10.7511/jslx201104007 |
| KeyWord:ill-conditioned algebraic equations ill-conditioned matrix precise integration method iterative algorithm exponential matrix algorithm |
| Author | Institution |
| 富明慧 |
中山大学 应用力学与工程系,广州 |
| 张文志 |
中山大学 应用力学与工程系,广州 |
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| Abstract: |
| An efficient method based on the idea of the precise integration method for solving ill-conditioned linear algebraic equations is presented. Similar to that the steady-state heat conduction equation can be regarded as the limit form of the transient heat conduction equation, the ill-conditioned algebraic equations with positive definite real coefficient matrix can be taken as a limit form of first-order ordinary differential equations with initial value problem. And on this basis, a precise integration method for solving ill-conditioned algebraic equations is established. The method has not only high precision but also high efficiency due to exponential rate of convergence. Additionally, the treatment of ill-conditioned algebraic equations with non-positive definite coefficient matrix is also discussed. Numerical examples show clearly the validity of the presented method. |