10. Cholesky Factorization
Nicholas John Higham · Society for Industrial and Applied Mathematics eBooks · 2002
The matrix of that equation system is negative definite—which is a positive definite system that has been multiplied through by −1. For all practical geometries the common finite difference Laplacian operator gives rise to these, the best of all possible matrices. Just about any standard solution method will succeed, and many theorems are available for your pleasure.