A subspace preconditioning algorithm for eigenvector/eigenvalue computation (Q675699)

The authors study a parallelizable technique, using subspace iteration and preconditioning, for computing a modest number of the smallest eigenvalues and the corresponding eigenvectors of a symmetric positive definite linear operator on a finite-dimensional real Hilbert space. The method involves a recursively generated sequence of subspaces and uses the Rayleigh-Ritz procedure. Estimates of its convergence rate are proved. A simple numerical example is considered and the method is compared with an earlier method of E. G. D'yakonov and the third author.