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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Performance of H-LU Preconditioning for Sparse Matrices

Lars Grasedyck, Wolfgang Hackbusch and Ronald Kriemann


In this paper we review the technique of hierarchical matrices and put it into the context of black-box solvers for large linear systems. Numerical examples for several classes of problems from medium to large scale illustrate the applicability and efficiency of this technique. We compare the results with those of several direct solvers (which typically scale quadratically in the matrix size) as well as an iterative solver (an algebraic multigrid method) which scales linearly (if it converges in O(1) steps).

MSC Codes:
65F05, 65F30, 65F50, 65N55
hierarchical matrices, black-box clustering, preconditioning, lu, direct solver, iterative solver, performance

Related publications

2008 Journal Open Access
Lars Grasedyck, Wolfgang Hackbusch and Ronald Kriemann

Performance of \(\mathscr {H}\)-LU preconditioning for sparse matrices

In: Computational methods in applied mathematics, 8 (2008) 4, pp. 336-349