The Acceleration And Preconditioning Techniques For Subspace Iteration Method

In this paper, we consider the subspace iteration method for solving large symmetric eigenproblems. In order to accelerate the convergence rate, we improve the original method with Chebyshev polynomials and preconditioning techniques, and present two new algorithms.The first one of the new algorithms is the accelerated subspace iteration method by using Chebyshev polynomials. The main part of this hybrid algorithm is a Chebyshev iteration which applies Chebyshev polynomials to act on initial vectors and makes the obtained vectors close to the wanted eigenvectors; The second one is the preconditioning subspace iteration method which uses a preconditioning matrix to impact the residual matrix obtained from the iteration procedure, so the distribution of eigenvalues is improved.We analyze the convergence of the new methods and give some results of numerical experiments in which we compare the new methods with the original subspace iteration method. Our numerical results show that the accelerated subspace iteration method by using Chebyshev polynomials and the preconditioning subspace iteration method are superior to the original subspace iteration method.