SVDdiagnostic, a program to diagnose numerical conditioning of Rietveld refinements

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DOIResolve DOI: http://doi.org/10.1107/S0021889806009915
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TypeArticle
Journal titleJournal of Applied Crystallography
Volume39
IssueJune 3
Pages458465; # of pages: 8
SubjectConcrete
AbstractWithin the scope of a continuing study involving parameterization of the apatite structure type, we needed to assess the relative numerical stability of crystallographic versus crystal-chemical least-squares Rietveld refinements. The corresponding undertaking turned out to be 'the tip of the iceberg' with respect to numerical analysis in relation to inversion of square, symmetrical crystallographic least-squares matrices. We ended up with a logically disjointed manuscript that one of the referees wisely suggested be split into two homogeneous parts referring to each other. In this part, we lay the mathematical base for evaluation of numerical stability by singular value decomposition (SVD)implement it, discuss it, and then draw conclusions.
Publication date
LanguageEnglish
AffiliationNational Research Council Canada; NRC Institute for Chemical Process and Environmental Technology; NRC Institute for Research in Construction
Peer reviewedYes
NRC number50566
19761
NPARC number20378299
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Record identifier76ee2e28-04cb-4c8c-a154-be455d92b44f
Record created2012-07-24
Record modified2016-05-09
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