Version 2.6.0

10th June 2020

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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 AX = B. This package uses OpenMP and is designed for multicore architectures. It computes the sparse Cholesky factorization

A = PL(PL)

where L = LT (real symmetric) or L = LH (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.