Purpose

SpLLT is a direct solver for solving large sparse symmetric positive-definite linear systems of equations:

\[AX=B\]

This is done by computing the Cholesky decomposition of the input matrix:

\[PAP^T=LL^T\]

where the factor \(L\) is a lower triangular matrix and the matrix \(P\) is a permutation matrix used to reduce the fill-in generated during the factorization. Following the matrix factorization the solution can be retrieved by successively solving the system \(LY=PB\) (forward substitution) and \(L^{T}PX=Y\) (backward substitutions).