Approximate inverse preconditioning in the parallel solution of sparse eigenproblems

A preconditioned scheme for solving sparse symmetric eigenproblems is propo sed. The solution strategy relies upon the DACG algorithm, which is a Preco nditioned Conjugate Gradient algorithm for minimizing the Rayleigh Quotient . A comparison with the well established ARPACK code shows that when a smal l number of the leftmost eigenpairs is to be computed, DACG is more efficie nt than ARPACK. Effective convergence acceleration of DACG is shown to be p erformed by a suitable approximate inverse preconditioner (AINV). The perfo rmance of such a preconditioner is shown to be safe, i.e. not highly depend ent on a drop tolerance parameter. On sequential machines, AINV preconditio ning proves a practicable alternative to the effective incomplete Cholesky factorization, and is mon efficient than Block Jacobi. Owing to its paralle lizability, the AINV preconditioner is exploited for a parallel implementat ion of the DACG algorithm, Numerical tests account for the high degree of p arallelization attainable on a Gray T3E machine and confirm the satisfactor y scalability properties of the algorithm. A final comparison with PARPACK shows the (relative) higher efficiency of AINV-DACG. Copyright (C) 2000 Joh n Wiley & Sons, Ltd.