预处理子空间迭代法

研究了计算大型稀疏对称矩阵的若干个最大或最小特征值的问题．首先引入求解大型对称特征值问题的预处理技术,给出了改善后的算法及相应的算法收敛分析．而求解特征值问题的子空间迭代法,当矩阵的特征值的分布范围较大时,其收敛速度会受到限制．为了加速子空间迭代法的收敛速度,对每次迭代所得的残余矩阵直接进行预处理以改善矩阵特征值的分布而加速收敛．讨论了预处理技术对子空间迭代法的应用,从而给出了预处理子空间迭代法．最后给出了数值例子,结果表明预处理子空间迭代法比子空间迭代法优越,不仅收敛速度快,并且减少了计算量和计算时间．

Preconditioning subspace iteration method

The problem of computing a few of the largest (or smallest) eigenvalues of a large sparse symmetric matrix is investigated. The preconditioning techniques for computing approximation of the large symmetric matrix are introduced, and improved algorithm and its convergence are presented. The convergence rate of subspace iteration method used to compute eigenvalues problem is confined when the distribution range of eigenvalues is large.In order to accelerate the convergence rate of the subspace iteration method, the preconditioning matrix is used to impact the residual matrix obtained from the iteration procedure, so the distribution of eigenvalues is improved. Having discussed the application of preconditioning techniques to the subspace iteration method, the preconditioning subspace iteration method is presented. Our numerical experiments show that the new method is more effective in convergence of algorithm. And it decreases the computation cost and computation time.