Performance of H-LU preconditioning for sparse matrices. (English) Zbl 1156.65042
Summary: 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 (algebraic multigrid) which scales linearly (if it converges in \(O(1)\) steps).
MSC:
65F35 | Numerical computation of matrix norms, conditioning, scaling |
65F05 | Direct numerical methods for linear systems and matrix inversion |
65F30 | Other matrix algorithms (MSC2010) |
65F50 | Computational methods for sparse matrices |
65N55 | Multigrid methods; domain decomposition for boundary value problems involving PDEs |