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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 $\mathbf{AX\; =\; B}$. This package uses OpenMP and is designed for multicore architectures. It computes the sparse Cholesky factorization

where ${\mathbf{<msup><mrow>L</mrow><mrow>\star </mrow></msup>\; =\; L}}^T$ (real symmetric) or ${\mathbf{<msup><mrow>L</mrow><mrow>\star </mrow></msup>\; =\; L}}^H$ (complex Hermitian), $\mathbf{P}$ is a permutation matrix and $\mathbf{L}$ 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 $\mathbf{A}$ 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 $\mathbf{A}$ is indefinite and pivoting for numerical stability is required, the package HSL_MA86 should be used.

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