## Version 2.4.0

9th May 2016

Recent Changes

• Single
• Double
• Single Complex
• Double Complex

### HSL_MA87 Sparse symmetric positive-deﬁnite system using OpenMP

HSL_MA87 uses a direct method to solve large sparse positive-deﬁnite symmetric linear systems of equations $AX=B$. This package uses OpenMP and is designed for multicore architectures. It computes the sparse Cholesky factorization

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

where ${{L}^{\star }=L}^{T}$ (real symmetric) or ${{L}^{\star }=L}^{H}$ (complex Hermitian), $P$ is a permutation matrix and $L$ is lower triangular.

The eﬃciency of HSL_MA87 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 indeﬁnite and pivoting for numerical stability is required, the package HSL_MA86 should be used.

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