求解线性方程组的投影算法

Method of Solving Linear Equations Based on Residual Space

分析了基于残差空间求解线性方程组的一维投影算法、最速下降法和最小剩余法。定义了长轴陷阱及陷阱深度,用它们刻划了2种算法迭代过程中锯齿现象的几何特征。给出了基于残差序列的避开长轴陷阱的扰动技巧,即投影算法。数值试验表明,投影算法要优于现在流行的主要求解线性方程组算法。

The one-dimension projection algorithm, which is the steepest descent method, based on residual space for solving linear equations is analyzed in this paper. The definitions of long axis trap and trap depth are given. The geometrical feature of the algorithm is characterized. The method of perturbation based on residual series, which keeps residuals off the long axis trap, is presented in this paper. That is the multidimension projection method. The numerical experimentation shows that the method is .superior to the present popular dominant algorithms.