Journal article
An algebraic approach for $${\mathcal{H}}$$ -matrix preconditioners
Computing, Vol.80(2), pp.169-188
06/2007
DOI: 10.1007/s00607-007-0224-4
Abstract
Hierarchical matrices (
$${\mathcal{H}}$$
-matrices) approximate matrices in a data-sparse way, and the approximate arithmetic for
$${\mathcal{H}}$$
-matrices is almost optimal. In this paper we present an algebraic approach for constructing
$${\mathcal{H}}$$
-matrices which combines multilevel clustering methods with
$${\mathcal{H}}$$
-matrix arithmetic to compute the
$${\mathcal{H}}$$
-inverse,
$${\mathcal{H}}$$
-LU, and the
$${\mathcal{H}}$$
-Cholesky factors of a matrix. Then the
$${\mathcal{H}}$$
-inverse,
$${\mathcal{H}}$$
-LU or
$${\mathcal{H}}$$
-Cholesky factors can be used as preconditioners in iterative methods to solve systems of linear equations. The numerical results show that this method is efficient and greatly speeds up convergence compared to other approaches, such as JOR or AMG, for solving some large, sparse linear systems, and is comparable to other
$${\mathcal{H}}$$
-matrix constructions based on Nested Dissection.
Details
- Title: Subtitle
- An algebraic approach for $${\mathcal{H}}$$ -matrix preconditioners
- Creators
- S Oliveira - Department of Computer Science University of Iowa 14 McLean Hall Iowa City USAF Yang - Department of Computer Science University of Iowa 14 McLean Hall Iowa City USA
- Resource Type
- Journal article
- Publication Details
- Computing, Vol.80(2), pp.169-188
- Publisher
- Springer-Verlag; Vienna
- DOI
- 10.1007/s00607-007-0224-4
- ISSN
- 0010-485X
- eISSN
- 1436-5057
- Language
- English
- Date published
- 06/2007
- Academic Unit
- Computer Science; Mathematics
- Record Identifier
- 9984002423302771
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