用Chebyshev多项式加速的预处理子空间迭代法

THE PRECONDITIONING SUBSPACE ITERATION METHOD ACCELERATED BY CHEBYSHEV ITERATION

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，首先引入了求解大型对称特征值问题的预处理子空间迭代法和Chebyshev迭代法，并对其作了理论分析．为了加速预处理子空间迭代法的收敛性，笔者采用组合Chebyshev迭代法和预处理子空间迭代法，提出了计算大型对称稀疏矩阵的几个最大或最小特征值的Chebyshev预处理子空间迭代法．数值结果表明，该方法比预处理子空间方法优越．

The problem of computing a few of the largest （or smallest） eigenvalues of a large symmetric sparse matrix is dealt with. This paper considers the preconditioning subspace iteration method and the Chebyshev iteration, and analyzes them. In order to accelerate the convergence rate of the preconditioning subspace iteration method,a new method, i. e. Chebyshev -PSI （the preconditioning subspace iteration） method, is presented for computing the extreme eigenvalues of a large symmetric sparse matrix. The new method combines the Chebyshev iteration with the PSI method. Numerical experiments show that the Chebyshev - PSI metod is very effective for computing the extreme eigenvalues of a large symmetric sparse matrix.