Premium
SVDdiagnostic , a program to diagnose numerical conditioning of Rietveld refinements
Author(s) -
Mercier Patrick H. J.,
Le Page Yvon,
Whitfield Pamela S.,
Mitchell Lyndon D.
Publication year - 2006
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s0021889806009915
Subject(s) - singular value decomposition , rank (graph theory) , reduction (mathematics) , condition number , matrix (chemical analysis) , stability (learning theory) , singular value , mathematics , computer science , arithmetic , algorithm , eigenvalues and eigenvectors , geometry , combinatorics , physics , chemistry , quantum mechanics , machine learning , chromatography
Within 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.Dans le cadre d'une \ue9tude continue faisant intervenir le param\ue9trage du type de structure d'apatites, nous avons d\ufb \ue9valuer la stabilit\ue9 num\ue9rique relative des affinements selon la m\ue9thode de Rietveld des moindres carr\ue9s, cristallographiques vs cristallochimiques. L'op\ue9ration correspondante s'est r\ue9v\ue9l\ue9e \ueatre la pointe de l'iceberg pour ce qui est de l'analyse num\ue9rique en relation avec l'inversion des matrices (carr\ue9es) des moindres carr\ue9s cristallographiques sym\ue9triques. Il en est r\ue9sult\ue9 un manuscrit scientifique logiquement non cons\ue9cutif, que l'un des examinateurs a judicieusement recommand\ue9 de s\ue9parer en deux parties homog\ue8nes renvoyant l'une \ue0 l'autre. Dans cette partie-ci, nous \ue9tablissons le fondement math\ue9matique de l'\ue9valuation de la stabilit\ue9 num\ue9rique par la d\ue9composition en valeurs singuli\ue8res (DVS), la mettons en application, l'examinons, puis en tirons des conclusions.Peer reviewed: YesNRC publication: Ye