Preconditioning Subspace Iteration Method Accelerated by Using Chebyshev Polynomial

The paper deals with the subspace iteration method for computing a few of the largest(or smallest) eigenvalues of a large sparse symmetric matrix. Firstly the Chebyshev iteration and the preconditioning techniques are considered for computing approximation of the large sparse matrix A,which accelerated the convergence rate of the subspace iteration method.In order to faster accelerate the convergence rate of the subspace iteration method.The Chebyshev polynomial and the preconditioning techniques are simultaneously used to the subspace iteration method,improving the preconditioned residual matrix with the Chebyshev polynomial.That is to discuss application of the Chebyshev iteration to the preconditioning subspace iteration method.This reduces the distribution range of eignvaluces and improves the starting matrix obtained from every iteration procedure.Then the preconditioning subspace iteration accelerated by using Chebyshev polynomial is presented.The numerical experiments show that the accelerated preconditioning subspace iteration method is more effective in convergence of algorithm than the original preconditioning subspace iteration method.And it decreases the computation cost and computation time.