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Ausgleichung mit singulärer Varianzkovarianzmatrix am Beispiel der geometrischen Deformationsanalyse / G. Nkuite (1998)
Titre : Ausgleichung mit singulärer Varianzkovarianzmatrix am Beispiel der geometrischen Deformationsanalyse Titre original : [Compensation avec une matrice de variance-covariance singulière : exemple de l'analyse de déformation géométrique] Type de document : Thèse/HDR Auteurs : G. Nkuite, Auteur Editeur : Munich : Bayerische Akademie der Wissenschaften Année de publication : 1998 Collection : DGK - C Sous-collection : Dissertationen num. 501 Importance : 85 p. Format : 21 x 30 cm ISBN/ISSN/EAN : 978-3-7696-9540-3 Note générale : Bibliographie Langues : Allemand (ger) Descripteur : [Vedettes matières IGN] Algèbre
[Termes IGN] axiome de Bayes
[Termes IGN] compensation
[Termes IGN] déformation géométrique
[Termes IGN] matrice de covariance
[Termes IGN] modèle linéaire
[Termes IGN] modèle stochastique
[Termes IGN] valeur aberranteRésumé : (Auteur) The principal subject matter of this work is the development and analysis of the theory for adjustment with singular variance covariance matrix (vcm) of observations. Further objectives are the development of a method for the localization of outliers and of a theory for modelling of the point noise by the congruency test.
The problem in linear model with singular vcm is the determination of a weight matrix to compute the weighted square of the residuals. This weight matrix depends on the choice of the g-inverse. To ensure the uniqueness of the weighted square of the residuals, a model space matrix of the observations that takes into account all information contained in the observations is defined.
To accelerate the localization of outliers in a linear model a method is presented that is based on the analysis of the sensitivity of the observations on the computation of adjusted observations and of the residuals.
For the computation of the separability measures, the changes of the weighted square of the residuals under different alternative hypotheses are used. To develop less sensitive hypothesis tests, two methods are derived. The first one is based on a modification of the stochastic model and the second one on the computation of test values by means of Bayesian statistics without change of the vcm of the observations. The singularity of the vcm means that the observations contain stochastic and non-stochastic information. It is shown that the use of the g-inverse of the singular vcm as weight matrix is only allowed if the column space of the design matrix is included in the column space of the vcm. The estimation of the parameters in the linear model with singular vcm does not depend on the rank of the vcm but on the rank of the design matrix. For the models of the geometrical deformation analysis (e.g. strain and block movement model) by which adjusted coordinates are used as observations, the design matrix is always column regular. Thus the parameters in these models are best linear unbiased estimable.Numéro de notice : 56305 Affiliation des auteurs : non IGN Thématique : MATHEMATIQUE Nature : Thèse étrangère Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=60001 Réservation
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