Extended version with the analysis of dynamic system for iterative refinement of solution
Extended version with the analysis of dynamic system for iterative refinement of solution
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DOI：
10.1080/00207160802247604
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发表时间：
2010-03
影响因子：
1.8
通讯作者：
Xinyuan Wu;Xiong You
中科院分区：
文献类型：
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作者：
Xinyuan Wu;Xiong You
本文给出了威尔金森迭代改进解的动力系统分析的扩展形式。结果表明，这种迭代改进可以看作是将步长h=1的显式Euler方法应用于具有唯一全局渐近稳定平衡点的动力系统，即具有非奇异矩阵A的线性系统Ax=B的解x*=A −1 B.通过跟踪线性常微分方程组的解曲线，提出了求解系数矩阵非奇异的病态线性代数方程组的一种扩展迭代改进方法.我们证明了无条件收敛性，并得到了推广的迭代加细过程的全面结果。数值实验表明，与威尔金森方法相比，该方法是有效的。
The extended version with the analysis of dynamic system for Wilkinson's iteration improvement of solution is presented in this paper. It turns out that the iteration improvement can be viewed as applying explicit Euler method with step size h=1 to a dynamic system which has a unique globally asymptotically stable equilibrium point, that is, the solution x*=A −1 b of linear system Ax=b with non-singular matrix A. As a result, an extended iterative improvement process for solving ill-conditioned linear system of algebraic equations with non-singular coefficients matrix is proposed by following the solution curve of a linear system of ordinary differential equations. We prove the unconditional convergence and derive the roundoff results for the extended iterative refinement process. Several numerical experiments are given to show the effectiveness and competition of the extended iteration refinement in comparison with Wilkinson's.