Abstract
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. (A correction to this article has been appended to the pdf file.)
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