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Auteur P. Lohse |
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Ausgleichungsrechnung in nichtlinearen Modellen / P. Lohse (1994)
Titre : Ausgleichungsrechnung in nichtlinearen Modellen Titre original : [Calcul de compensation dans les modèles non linéaires] Type de document : Thèse/HDR Auteurs : P. Lohse, Auteur Editeur : Munich : Bayerische Akademie der Wissenschaften Année de publication : 1994 Collection : DGK - C Sous-collection : Dissertationen num. 429 Importance : 131 p. Format : 21 x 30 cm ISBN/ISSN/EAN : 3-7696-9472-7 Note générale : Bibliographie Langues : Allemand (ger) Descripteur : [Vedettes matières IGN] Analyse numérique
[Termes IGN] modèle de Gauss-Markov
[Termes IGN] modèle non linéaire
[Termes IGN] programmation non linéaireRésumé : (Auteur) Within the framework of this thesis adjustment is investigated according to the least squares method in a nonlinear Gauss-Markoff model. The minimization of the least squares criterion regularly results in a solution of an optimization problem. The necessary condition for a local minimum (optimality of the first order) leads to the system of nonlinear normal equations. The sufficient condition for a local minimum (optimality of the second order) provides information about the admissibility of the least squares method. By means of the geometrical analysis of the minimum problem it is possible to successfully present a clear interpretation of the optimality criteria.
Methods for the determination of the total solution set of a nonlinear algebraic system of normal equations are elucidated. Subsequently there follows the geometrical discussion of the Gaufi-Newton Method as well as the Newton-Raphson Method, two methods of different order of differentiation for the iterative refinement of an initial approximation value.
Using the example of the resection problem (with distances) the results of the theoretical conside--rations are confirmed. Special emphasis is thereby placed on the determination of the total solution set of the system of normal equations as well as on the admissible solutions of the minimum pro-blem. Two methods are put forward for the computation of suitable initial values in the case of the iterative solution of the system of normal equations.
The final part of the work consists of a discussion regarding the geodetic resection and intersection problems with respect to the model choice and to the nonlinear normal equations.Numéro de notice : 28059 Affiliation des auteurs : non IGN Thématique : MATHEMATIQUE Nature : Thèse étrangère Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=63406 Exemplaires(2)
Code-barres Cote Support Localisation Section Disponibilité 28059-01 23.40 Livre Centre de documentation Mathématiques Disponible 28059-02 23.40 Livre Centre de documentation Mathématiques Disponible