## Version 1.6.0

26th September 2016

Recent Changes

• Single
• Double
• Single Complex
• Double Complex

### 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

$A=PLD{\left(PL\right)}^{\star }$

where ${L}^{\star }={L}^{T}$ (real symmetric or complex symmetric) or ${L}^{\star }={L}^{H}$ (complex Hermitian, where ${L}^{H}$ 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.

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