• STFC home
  The Science and Technology Facilities Council
• HSL home
  About the HSL Mathematical Software Library
• HSL 2011
  Our current release
• HSL archive
  Older packages available at no cost
• Academic access
  Free access for teaching and research
• The Numerical Analysis Group
  About the research group behind HSL
• Contact us
  Our contact details

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

where ${L^{\star }=L}^T$ (real symmetric) or ${L^{\star }=L}^H$ (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.

.