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Truncation of Small Matrix Elements Based on the Euclidean Norm for Blocked Data StructuresPrimeFaces.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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2009 (English)In: Journal of Computational Chemistry, ISSN 0192-8651, E-ISSN 1096-987X, Vol. 30, no 6, p. 974-977Article in journal (Refereed) Published
##### Abstract [en]

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

2009. Vol. 30, no 6, p. 974-977
##### Keywords [en]

sparsity, linear scaling, Hartree-Fock, DFT, density functional theory, blocked data structure, Euclidean norms, Lanczos, sparse matrix, Frobenius norm, electronic-structure calculations, consistent-field theory, density-matrix, expansion methods, diagonalization, minimization, purification, search
##### National Category

Theoretical Chemistry
##### Identifiers

URN: urn:nbn:se:kth:diva-18301DOI: 10.1002/jcc.21120ISI: 000264651200015PubMedID: 18816463Scopus ID: 2-s2.0-65449174900OAI: oai:DiVA.org:kth-18301DiVA, id: diva2:336347
#####

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##### Note

QC 20100817Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2020-03-09Bibliographically approved
##### In thesis

Methods for the removal of small symmetric matrix elements based on the Euclidean norm of the error matrix are presented in this article. In large scale Hartree-Fock and Kohn-Sham calculations it is important to be able to enforce matrix sparsity while keeping errors under control. Truncation based on some unitary-invariant norm allows for control of errors in the occupied subspace as described in (Rubensson et al. J Math Phys 49, 032103). The Euclidean norm is unitary-invariant and does not grow intrinsically with system size and is thus suitable for error control in large scale calculations. The presented truncation schemes repetitively use the Lanczos method to compute the Euclidean norms of the error matrix candidates. Ritz value convergence patterns are utilized to reduce the total number of Lanczos iterations.

1. Matrix Algebra for Quantum Chemistry$(function(){PrimeFaces.cw("OverlayPanel","overlay114034",{id:"formSmash:j_idt841:0:j_idt848",widgetVar:"overlay114034",target:"formSmash:j_idt841:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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