Leftmost eigenvalue of real and complex sparse matrices on parallel computer using approximate inverse preconditioning

An efficient parallel approach for the computation of the eigenvalue of smallest absolute magnitude of sparse real and complex matrices is provided. The proposed strategy tries to improve the efficiency of the reverse power method. At each inverse power iteration the linear system is solved either by the conjugate gradient scheme (symmetric case) or by the Bi-CGSTAB method (symmetric case). Both solvers are preconditioned employing the approximate inverse factorization and thus are easily parallelized. The satisfactory speed-ups obtained on the CRAY T3E supercomputer show the high degree of parallelization reached by the proposed algorithm.