病态线性方程组的新解法:误差转移法

基金项目: 广东省自然科学基金资助项目 (99415 1)

A New Method for Solving l- Conditioned Linear Systems

摘要: 提出了一种求解病态线性方程组的简便有效的新算法，它的主要思想是将直接求解法中的计算误差转移到一个中间量上，从而使得最终解获得很好的精度，因此可极大地缓解一般算法条件预优的困难以及病态方程组的求解难度。数值计算的结果表明，算法对极其病态的线性方程组也可获得较好的精度和稳定性。
- 经性方程组 /
- 病态方程 /
- 求解法 /
- 误差转移法
Abstract: A new simple and effective method for solving ill conditioned linear systems is presented in this paper. This method tried mainly not to decrease the error caused in direct solving, instead, it tried to transfer this error to a medium variable. An algorithm based on this method was presented, and examples showed that this algorithm could solve extremely ill conditioned linear systems correctly and stably.
- linear systems /
- ill conditioned /
- error analysis

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