References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt152",{id:"formSmash:upper:j_idt152",widgetVar:"widget_formSmash_upper_j_idt152",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt153_j_idt156",{id:"formSmash:upper:j_idt153:j_idt156",widgetVar:"widget_formSmash_upper_j_idt153_j_idt156",target:"formSmash:upper:j_idt153:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

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, 104105- p.Article in journal (Refereed) Published
##### Abstract [en]

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

2008. Vol. 128, no 10, 104105- p.
##### 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: 000254025300007ScopusID: 2-s2.0-40849134177OAI: oai:DiVA.org:kth-9446DiVA: diva2:114025
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt455",{id:"formSmash:j_idt455",widgetVar:"widget_formSmash_j_idt455",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt461",{id:"formSmash:j_idt461",widgetVar:"widget_formSmash_j_idt461",multiple:true});
#####

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

QC 20100908Available from: 2008-11-04 Created: 2008-11-04 Last updated: 2010-09-08Bibliographically 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_idt731:0:j_idt735",widgetVar:"overlay114034",target:"formSmash:j_idt731:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1196",{id:"formSmash:lower:j_idt1196",widgetVar:"widget_formSmash_lower_j_idt1196",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1197_j_idt1199",{id:"formSmash:lower:j_idt1197:j_idt1199",widgetVar:"widget_formSmash_lower_j_idt1197_j_idt1199",target:"formSmash:lower:j_idt1197:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});