Sparse approximate inverses and target matrices

Journal article

If P has a prescribed sparsity and minimizes the Frobenius norm |I - PA||F, it is called a sparse approximate inverse of A. It is well known that the computation of such a matrix P is via the solution of independent linear least squares problems for the rows separately (and therefore in parallel). In this paper we consider the choice of other norms and introduce the idea of "target" matrices. A target matrix, T, is readily inverted and thus forms part of a preconditioner when ||T - PA|| is minimized over some appropriate sparse matrices P. The use of alternatives to the Frobenius norm which maintain parallelizability, while discussed in early literature, does not appear to have been exploited. © 2005 Society for Industrial and Applied Mathematics.

Authors: Holland, R; Wathen, A; Shaw, G

• Publication status: Published
• Journal: SIAM JOURNAL ON SCIENTIFIC COMPUTING
• Volume: 26
• Issue: 3
• Pages: 1000-1011
• Publication date: 2005-01-01
• DOI: 10.1137/030601132
• EISSN: 1095-7197
• ISSN: 1064-8275
• Language: English
• Keywords: preconditioning; sparse approximate inverses; target matrices