Version 1.6.0

26th September 2016

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HSL_MA86 Sparse symmetric indefinite system using OpenMP

HSL_MA86 uses a direct method to solve large sparse symmetric indefinite linear systems of equations AX = B. This package uses OpenMP and is designed for multicore architectures. It computes the sparse factorization


where L = LT (real symmetric or complex symmetric) or L = LH (complex Hermitian, where LH denotes the conjugate transpose of L), P is a permutation matrix, L is unit lower triangular, and D is block diagonal with blocks of size 1 × 1 and 2 × 2.

The efficiency of HSL_MA86 is dependent on the user-supplied elimination order. The HSL package HSL_MC68 may be used to obtain a suitable ordering.

The lower triangular part of A must be supplied in compressed sparse column format. The HSL package HSL_MC69 may be used to convert data held in other sparse matrix formats and also to check the user’s matrix data for errors.

If A is known to be positive definite (so that pivoting for numerical stability is not required), we recommend HSL_MA87.