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MiS Preprint

Construction and Arithmetics of $\mathcal{H}$-Matrices

Lars Grasedyck and Wolfgang Hackbusch


In previous papers a class of H-matrices was introduced which are data-sparse and allow an approximate matrix arithmetic of nearly optimal complexity. In this paper we analyse the complexity (storage, addition, multiplication and inversion) of the H-matrix arithmetics. Two criteria, the sparsity and idempotency, are sufficient to give the desired bounds. For standard finite element and boundary element applications we present a construction of an H-matrix format for which we can give explicit bounds for the sparsity and idempotency.

MSC Codes:
65F05, 65F30, 65F50
hierarchical matrices, data-sparse approximations, fast solvers, formatted matrix operations

Related publications

2003 Repository Open Access
Lars Grasedyck and Wolfgang Hackbusch

Construction and arithmetics of \(\mathscr {H}\)-matrices

In: Computing, 70 (2003) 4, pp. 295-334