Richardson迭代法的松弛策略

将Richardson迭代法拓展应用于更一般的线性方程组求解中. 先用相似变换矩阵对迭代过程和迭代矩阵进行重新表示, 基于使迭代矩阵的谱半径达到极小值, 给出最优松弛参数的取值方法; 然后针对最小特征值难计算的问题, 提出一种仅依赖于最大特征值的加速收敛策略.

Relaxation Strategy for Richardson Iterative Method

The Richardson iterative method was extended to solve more general linear equations. First, the iterative process and the iterative matrix were reformulated by using the similar transformation matrix, based on minimizing spectral radius of the iterative matrix, and the method of selecting the optimal relaxation parameter was given. Then aiming at the problem that the smallest eigenvalue wasdifficult to calculate, an accelerated convergence strategy was proposed, which only depended on the largest eigenvalue.