ALGORITHMS FOR CONSTRUCTION OF PRECONDITIONERS BASED ON INCOMPLETE BLOCK-FACTORIZATIONS OF THE MATRIX

When applying an incomplete block-factorization technique sparse approximate inverses are needed for the successive Schur complements computed throughout the factorization. This paper proposes a method for the construction of such sparse approximate inverses. The method has an advantage over earlier versions, in that such approximate inverses of block-tridiagonal matrices can be computed in parallel. Comparative numerical experiments for solving a number of discretized diffusion equations by this preconditioning matrix in a preconditioned conjugate gradient method and earlier versions of incomplete block-factorization preconditioners are presented.