Wilkinson迭代改善的推广—定向扰动法

Generalization of wilkinson Iterative Refinement-Directional Perturbation Method

Wilkinson迭代改善是解病态线性方程组,提高解的精度的一个重要方法。本文从讨论它与松弛法的关系入手,引进另一种意义下的松弛方式一定向扰动法,并从理论上分析了该方法的实质是可应用于一般线性(超定或适定)方程组的由点到块逐步扩大的松弛,在超定的情况下最终可导出该组之Tchebychev解,在适定的情况下则等价于Wilkinson迭代改善。我们编制了定向扰动法的应用程序,分别对二种情况都给出了算例。此外本文的论证还推广文[4]的结果到rank(A)<n的情况。

Wilkinson Iterative Refinement is an important method for solving ill-conditioned linear system Ax=y. In this paper) its relationships with the well-known relaxation methods and the Directional Perturbation method which can be used for the solution of an over-determination system of linear equations in L_2-norm and L_∞-norm are diseusscd. It is proved that the Directional Perturbation method is a generalized form of wilkinson Iterative Refinement when A∈r^(mx)', where r=rank(A) ≤n≤m. Two numerical examples are given,