Anton Artemov
Scientific Computing
Department of Information Technology, Uppsala University
We consider three algorithms for inverse factorization of symmetric positive definite matrices, namely recursive inverse Cholesky, recursive inverse factorization and iterative refinement with a scaled identity. Although the algorithms should be generally applicable, this work was mainly motivated by the need for efficient and scalable inverse factorization of the basis set overlap matrix in large scale electronic structure calculations.
We show that for such matrices the computational cost increases only linearly with system size, describe parallelization within the Chunks and Tasks programming model, derive the critical path length estimations. The weak scaling behaviour of the algorithms is demonstrated and a theoretical justification of the scaling behaviour based on critical path length estimation is given.