A refined shifted block inverse-free Krylov subspace method for symmetric generalized eigenvalue problems

For computing the pp smallest eigenvalues and their corresponding eigenvectors of symmetric generalized eigenproblems simultaneously, Quillen and Ye have introduced a block inverse-free preconditioned Krylov subspace method (Quillen and Ye, 2010)  [14]. To accelerate convergence and compute interior eigenpairs, in this paper we present a refined shifted block inverse-free Krylov subspace algorithm based on the block Arnoldi process that generates a BB-orthogonality basis of the matrix Krylov subspace. It is proved that this algorithm can guarantee the convergence if the corresponding Ritz values converge. Numerical experiments show that the refined algorithm is more efficient than the original approach.