Factorized approximate inverse preconditioning of a sparse eigensolver

We exploit an optimization method, called DACG, which sequentially computes the smallest eigenpairs of a symmetric, positive definite, generalized eigenproblem, by CG minimizations of the Rayleigh quotient over subspaces of decreasing size. In this paper we analyze the effectiveness of the approximate inverse preconditioners, AINV and FSAI as DACG preconditioners for the solution of Finite Element and Finite Difference eigenproblems. Numerical tests on a Cray T3E Supercomputer were performed, showing the high degree of parallelism attainable by the code. We found that AINV and FSAI are both effective preconditioners for our DACG algorithm. Keywords: generalized eigenproblems, sparse approximate inverses, parallel algorithms. 1 Introduction. An important task in many scientific applications is the computation of a small number of the leftmost eigenpairs (the smallest eigenvalues and corresponding eigenvectors) of the problem Ax = s Bx; where A and B are large, sparse, symmetric positiv