A Chebyshev-Davidson Algorithm for Large Symmetric Eigenproblems

A polynomial filtered Davidson-type algorithm is proposed for symmetric eigenproblems, in which the correction-equation of the Davidson approach is replaced by a polynomial filtering step. The new approach has better global convergence and robustness properties when compared with standard Davidson-type methods. The typical filter used in this paper is based on Chebyshev polynomials. The goal of the polynomial filter is to amplify components of the desired eigenvectors in the subspace, which has the effect of reducing both the number of steps required for convergence and the cost in orthogonalizations and restarts. Numerical results are presented to show the effectiveness of the proposed approach.