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Construction and Arithmetics of
Lars Grasedyck and Wolfgang Hackbusch
Abstract
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.
- Received:
- 28.11.02
- Published:
- 28.11.02
- MSC Codes:
- 65F05, 65F30, 65F50
- Keywords:
- hierarchical matrices, data-sparse approximations, fast solvers, formatted matrix operations