新预条件下Jacobi迭代法的比较性定理

A New Comparison Theorem for the Preconditioned Jacobi Iterative Method

讨论了新预条件下Jacobi迭代法的收敛性.证明在严格对角占优的L-矩阵条件下,该预条件加快了Jacobi迭代法的收敛速度,而且在该预条件下Jacobi迭代法的谱半径是单调下降的.最后用数值例子验证本文得出的结论的正确性.

In this paper, the convergence analysis for a new preconditioned Jacobi iterative method was discussed.If the coefficient matrix is the strictly dominant L-matrix,the convergence rate of the precondilioned Jaeobi iterative method is faster than one of the Jacobi methods.In addition,the spectral radius of this method is monotonically decreasing.Last, a numerical example is used to verify the correctness of our theoretical resuhs.