Yun, Jae Heon Performance of ILU factorization preconditioners based on multisplittings. (English) Zbl 1040.65032 Numer. Math. 95, No. 4, 761-779 (2003). The author investigates the parallelizability of incomplete LU (ILU) preconditioners for sparse block tridiagonal H matrices. Preconditioned Krylov subspace methods are generally necessary to speed up convergence. But the ILU factorization does not lend itself to parallelization. However, if the multisplitting method converges, then \(P^{-1}\) (with \(PA = I-H\) and an iteration matrix \(H\) with spectral radius less than 1) is a good preconditioner for the Krylov method. Such a preconditioner \(P\) is derived from the multisplitting of the block diagonal H-matrix and it can be used in parallel in the preconditioner solver step to advantage. The convergence of such a scheme is studied, as well as the parallel performance for the ILU preconditioned BiCGSTAB algorithm. Reviewer: Frank Uhlig (Auburn) Cited in 11 Documents MSC: 65F10 Iterative numerical methods for linear systems 65F50 Computational methods for sparse matrices 65F35 Numerical computation of matrix norms, conditioning, scaling 65Y05 Parallel numerical computation Keywords:block triangular matrix; preconditioner; linear equation; Krylov subspace method; multisplitting; parallel algorithm; sparse matrix; incomplete LU factorization; convergence; H-matrix; BiCGSTAB algorithm PDFBibTeX XMLCite \textit{J. H. Yun}, Numer. Math. 95, No. 4, 761--779 (2003; Zbl 1040.65032) Full Text: DOI