关于外推Gauss-Seidel迭代法的收敛速度比较

Comparison of the Convergence Rates of the Gauss-Seidel Iteration and the Extrapolation Gauss-Seidel Iteration

给出了一定条件下的外推Gauss Seidel迭代法的最优外推参数和谱半径,并深入细致的讨论了Gauss Seidel迭代法和外推Gauss Seidel迭代法的收敛速度的比较,证明了在一定的条件下,最优外推Gauss Seidel迭代法总是比Gauss Seidel迭代法收敛的快.并给出了简单的数值例子以说明此结果.

In this paper, we gave the best extrapolation parameter and spectral radius of the extrapolation Gauss-Seidel iterative method under certain conditions. And we investigated further comparison of the convergence rates of the Gauss-Seidel iteration and the extrapolation Gauss-Seidel iteration. In the end, we presented two numerical examples to state our results.