## Version 1.1.0

19th April 2016

Recent Changes

• Single
• Double

### HSL_MP54 Parallel Cholesky solver

For a matrix that is full, symmetric and positive deﬁnite, this package performs parallel partial and complete factorisations and solutions of corresponding sets of equations, using OpenMP.

We consider the factorization

$A=\left(\begin{array}{cc}\hfill {A}_{11}\hfill & \hfill {A}_{21}^{T}\hfill \\ \hfill {A}_{21}\hfill & \hfill {A}_{22}\hfill \end{array}\right)=\left(\begin{array}{cc}\hfill {L}_{11}\hfill & \hfill \hfill \\ \hfill {L}_{21}\hfill & \hfill I\hfill \end{array}\right)\left(\begin{array}{cc}\hfill I\hfill & \hfill \hfill \\ \hfill \hfill & \hfill {S}_{22}\hfill \end{array}\right)\left(\begin{array}{cc}\hfill {L}_{11}^{T}\hfill & \hfill {L}_{21}^{T}\hfill \\ \hfill \hfill & \hfill I\hfill \end{array}\right)={LSL}^{T}$

where $A$ is order $n$, ${L}_{11}$ is lower triangular and both ${A}_{11}$ and ${L}_{11}$ have order $p\le n$.

Subroutines are also provided for the complementary partial forward and backward substitutions, that is, solving

$LX=B\phantom{\rule{1em}{0ex}}and\phantom{\rule{1em}{0ex}}{L}^{T}X=B.$

.