董书玲^*

（  辽宁工程技术大学理学院；  ）

摘要： 求解线性方程组的方法一般有高斯消去法，矩阵三角分解法，迭代法等。但一般的求解方法在处理病态线性方程组时，往往会变得不准确，甚至出现远远偏离真实解的情况。本文主要是将直接解法与迭代法结合起来，以使其达到较为精确的解。最后将得到的解作为初始值，进行优化，每个解给一个扰动范围，利用局部搜索法，将最小二乘原则作为停止规则，得到更为精确的解。
关键词： 病态线性方程组；混合算法；迭代；优化设计

Dong Shuling^*

（  Liaoning Technical University, Science college；  ）

Abstract： Methods for solving linear equations are generally Gaussian elimination, matrix triangular decomposition, iterative method. However, in dealing with a general solution of linear equations when they are ill, often fatally accurate, even far from the true solution to the situation. This paper gives the direct method that combined with the iterative method, to make it fairer and more accurate .Finally, let the solution as the initial value, to optimize the scope of each solution to a perturbation, through using local search method and the least squares principle as stopping rule, inorder to get the more accurate solution.

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