. The sparse inverse subset problem is the computation of the entries of the inverse of a sparse matrix for which the corresponding entry is nonzero in the factors of the matrix. We present a parallel, block-partitioned formulation of the inverse multifrontal algorithm to compute the sparse inverse subset. Numerical results for an implementation of this algorithm on an 8-processor, sharedmemory Cray-C98 architecture are discussed. We show that for large problems we obtain efficiency ratings of over 80% and performance in excess of 1 Gflop. 1. Introduction. An efficient method to compute the sparse inverse subset (Zsparse) is important in practical applications such as the computation of short circuit currents in power systems or in estimating the variances of the fitted parameters in the least-squared data-fitting problem. (The sparse inverse subset (Zsparse), is defined as the set of inverse entries in locations corresponding to the positions of nonzero entries in the LDU factorize...

We present the symmetric inverse multifrontal method for computing the sparse inverse subset of symmetric matrices. The symmetric inverse multifrontal approach uses an equation presented by Takahashi, Fagan, and Chin to compute the numerical values of the entries of the inverse, and an inverted form of the symmetric multifrontal method of Duff and Reid to guide the computation. We take advantage of related structures that allow the use of dense matrix kernels (levels 2 & 3 BLAS) in the computation of this subset. We discuss the theoretical basis for this new algorithm and give numerical results for a serial implementation and demonstrate its performance on a Cray-C98.