STFC Website

part of UK Research & Innovation

Version 2.8.1

1st November 2023

HSL_MA97: Sparse symmetric system using OpenMP

HSL_MA97 uses a direct method to solve large sparse symmetric linear systems of equations \(\mathbf{AX = B}\). This package optionally uses OpenMP and is designed to achieve bit-compatible results regardless of the number of threads used. It computes the sparse factorization \[\mathbf{A = PLD(PL)^\star} \qquad \mbox{(Indefinite)}\] or \[\mathbf{A = PLL^\star P^T} \qquad \mbox{(Positive-definite)}\] where \(\mathbf{L^{\star}} = \mathbf{L}^T\) (real symmetric or complex symmetric) or \(\mathbf{L}^{\star} = \mathbf{L}^H\) (complex Hermitian, where \(\mathbf{L}^H\) denotes the conjugate transpose of \(\mathbf{L}\)), \(\mathbf{P}\) is a permutation matrix, \(\mathbf{L}\) is lower triangular, and \(\mathbf{D}\) is block diagonal with blocks of size \(1 \times 1\) and \(2 \times 2\).

If \(\mathbf{A}\) is large, bit-compatible answers are not required, we recommend using HSL_MA86 or HSL_MA87 instead for better efficiency.