Zhang, Jun Sparse approximate inverse and multilevel block ILU preconditioning techniques for general sparse matrices. (English) Zbl 0966.65043 Appl. Numer. Math. 35, No. 1, 67-86 (2000). A preconditioning technique for general sparse matrices, which combines a multilevel block ILU (BILUM) with the sparse approximate inverse techniques, is presented.The two basic methods are introduced and the resulting preconditioner is designed to have the ability of controlling sparsity and increased parallelism compared to the standard BILUM preconditioner. Extensive numerical experiments with a discretized convection-diffusion problem and five additional, well-known matrices from different sparse matrix collections illustrate the behaviour of the proposed preconditioner, but also the realization that it is unlikely that there exists a general purpose preconditioner being superior for all types of problems. Reviewer: René Lamour (Berlin) Cited in 6 Documents MSC: 65F35 Numerical computation of matrix norms, conditioning, scaling 65F10 Iterative numerical methods for linear systems 65F50 Computational methods for sparse matrices Keywords:incomplete LU factorization; sparse approximate inverse; Krylov subspace methods; preconditioning; sparse matrices; numerical experiments; convection-diffusion problem Software:BILUM; BILUTM; ILUM; BPKit; SparseMatrix PDFBibTeX XMLCite \textit{J. Zhang}, Appl. Numer. Math. 35, No. 1, 67--86 (2000; Zbl 0966.65043) Full Text: DOI