## Version 2.6.3

1st August 2022

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 $$\mathbf{AX = B}$$. This package uses OpenMP and is designed for multicore architectures. It computes the sparse Cholesky factorization $\mathbf{ A = PL(PL)^\star}$ where $$\mathbf{L^{\star} = L}^T$$ (real symmetric) or $$\mathbf{L^{\star} = L}^H$$ (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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