Recursive inverse factorization
2008 (English)In: Journal of Chemical Physics, ISSN 0021-9606, E-ISSN 1089-7690, Vol. 128, no 10, 104105- p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
2008. Vol. 128, no 10, 104105- p.
Hermitian matrices, matrix decomposition, recursion method, sparse matrices, congruence transformation, inverse factorization, iterative refinement
IdentifiersURN: urn:nbn:se:kth:diva-9446DOI: 10.1063/1.2884921ISI: 000254025300007ScopusID: 2-s2.0-40849134177OAI: oai:DiVA.org:kth-9446DiVA: diva2:114025
QC 201009082008-11-042008-11-042010-09-08Bibliographically approved