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Recursive inverse factorizationPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2008 (English)In: Journal of Chemical Physics, ISSN 0021-9606, E-ISSN 1089-7690, Vol. 128, no 10, p. 104105-Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

2008. Vol. 128, no 10, p. 104105-
##### Keyword [en]

Hermitian matrices, matrix decomposition, recursion method, sparse matrices, congruence transformation, inverse factorization, iterative refinement
##### National Category

Theoretical Chemistry
##### Identifiers

URN: urn:nbn:se:kth:diva-9446DOI: 10.1063/1.2884921ISI: 000254025300007Scopus ID: 2-s2.0-40849134177OAI: oai:DiVA.org:kth-9446DiVA, id: diva2:114025
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt467",{id:"formSmash:j_idt467",widgetVar:"widget_formSmash_j_idt467",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt473",{id:"formSmash:j_idt473",widgetVar:"widget_formSmash_j_idt473",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt479",{id:"formSmash:j_idt479",widgetVar:"widget_formSmash_j_idt479",multiple:true});
##### Note

QC 20100908Available from: 2008-11-04 Created: 2008-11-04 Last updated: 2017-12-14Bibliographically approved
##### In thesis

A^{ }recursive algorithm for the inverse factorization *S*^{−1}=*Z**Z*^{*} 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.

1. Matrix Algebra for Quantum Chemistry$(function(){PrimeFaces.cw("OverlayPanel","overlay114034",{id:"formSmash:j_idt787:0:j_idt791",widgetVar:"overlay114034",target:"formSmash:j_idt787:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

doi
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