列扰动的线性方程组的ABS算法

On ABS Algorithms for Column Perturbed Linear Systems

本文讨论在用ABS算法求得某线性方程组的解之后,如何有效地利用求解过程中所得到的信息,求解增加若干个变量或减少若干个变量所得到的新的方程组。本文的算法是基于ABS算法而提出的,它们适用于反复求解不断增加变量和减少变量的问题。计算量分析表明,与完全重新求解新方程组比较,本文所提出的方法可以较多地节省计算量。

One of the most interesting problems in numerical analysis and numerical optimization is to solve a linear system of equations. Sometimes it should be repeated when some unknowns are deleted or added. In this paper, two algorithms which are based on the ABS class are proposed for the above problems respectively. After the original liner system has been solved, the algorit proposed here can efficiently solve the new system which is obtained from the original one by deleting or adding some unknowns by using the information obtained in the previous computation. In addition, these algo- rithms can be used continually when some unkown are deleted or added successively with less com- putation effort.