用Chebyshev多项式加速的子空间迭代法

研究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子空间迭代法和Chebyshev迭代法，并对后者作了理论分析。为了加速子空间迭代法的收敛速度，作者用Chebyshev多项式来改进原始的子空间迭代法，即讨论Chebyshev迭代法对子空间迭代法的应用，从而给出了Chebyshev-子空间迭代法。最后把原始的方法和改进的方法计算数值例子的结果进行了比较，其结果表明Chebyshev-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。

Subspace Iteration Accelerated by Using Chebyshev Polynomials

The problem of computing a few of the largest (or smallest) eigenvalues of a large sparse symmetric matrix is dealt withe. This paper considers the original subspace iteration method for computing approximation of the large sparse matrix A and the Chebycshev iteration, and analyzes the convergence of the latter. In order to accelerate the convergence rate of the subspace iteration method, the paper improves the subspace iteration original method with the Chebyshev Polynomial, discusses application of the Chebyshev iteration to the subspace iteration method and presents the Chebyshev subspace iteration method. Numerical experiments show that the accelerated subspace iteration method by using Chebyshev Polynomial is more effective in convergence of algorithm than the original subspace iteration method. So it decreases the computation cost and computation time.