Linear‐scaling Cholesky decomposition

Abstract

We present linear-scaling routines for the calculation of the Cholesky decomposition of a symmetric positive-definite matrix and its inverse. As an example, we consider the inversion of the overlap matrix of DNA and amylose fragments as well as of linear alkanes, where the largest system corresponds to a 21,442 x 21,442 matrix. The efficiency and the scaling behavior are discussed and compared to standard LAPACK routines. Our Cholesky routines are publicly available on the web.