一类解线性方程组的有效的直接算法

A Class of Direct and Effective Methods for Solving Linear Systems

给出一类解线性方程组的直接方法。将此方法通过引入等价的方程组,从改善方程组的条件数入手,使得对病态的方程组有较好的精度。计算结果表明了该算法的可行性。

Based On Huang Method, a class of improved methods is given for solving ill-conditioned linear systems directly and effectively. A nOnsingular upper triaugular matrix R, formed and revised step by step in the process of iteration, is introduced. The linear independence of matrix AR's column vectors is much stronger than that of the original coefficient matrix A. The solution space of the systems is not changed, therefore the column vectors of matrix AR Can be used to obtain a good orthogonal basis of the systems with ordinary orthogonal method and finally the solution of the systems. Numerical examples show that these methods are more efficient than ordinary orthogonal methods.