解线性方程组的Jacobi迭代法和投影法之比较

Comparison between Projection Methods and Jacobi Iterations for System of Linear Equations

从线性方程组的多参数投影法推出Jacobi迭代法。从最优化的观点分析了Jacobi迭代法收敛速度较慢的原因 ,即其下降矩阵与步长向量两者并非最优组合。

In this paper, Jacobi iteration methods for system of linear equations are derived from mulitparameter projection methods. The reason why Jacobi iteration methods converge slower are researched on the view of optimization i.e.,its descent matrices and stepsize vectors are not optimization combinations.