title: Recursive inverse factorization.
abstract: A recursive algorithm for the inverse factorization S(-1)=ZZ(*) of Hermitian positive definite matrices S is proposed. The inverse factorization is based on iterative refinement [A.M.N. Niklasson, Phys. Rev. B 70, 193102 (2004)] combined with a recursive decomposition of S. As the computational kernel is matrix-matrix multiplication, the algorithm can be parallelized and the computational effort increases linearly with system size for systems with sufficiently sparse matrices. Recent advances in network theory are used to find appropriate recursive decompositions. We show that optimization of the so-called network modularity results in an improved partitioning compared to other approaches. In particular, when the recursive inverse factorization is applied to overlap matrices of irregularly structured three-dimensional molecules.
authors.affiliation: Department of Theoretical Chemistry, School of Biotechnology, Royal Institute of Technology, Stockholm, Sweden. emanuel@theochem.kth.se
authors.forename: Emanuel H
authors.initials: EH
authors.lastname: Rubensson
authors.forename: Nicolas
authors.initials: N
authors.lastname: Bock
authors.forename: Erik
authors.initials: E
authors.lastname: Holmström
authors.forename: Anders M N
authors.initials: AM
authors.lastname: Niklasson
mesh_terms: D000465:Algorithms; D019295:Computational Biology / Q000379:methods*; D003198:Computer Simulation; D008962:Models, Theoretical