Centre de documentation
scientifique

Ausgleichung großer geodätischer Netze mit Verfahren für schwach besetzte Matrizen / Hans-Jörg Schek (1977)

Public Titre : Ausgleichung großer geodätischer Netze mit Verfahren für schwach besetzte Matrizen Titre original : [Compensation de grands réseaux géodésiques avec des méthodes pour les matrices creuses] Type de document : Monographie Auteurs : Hans-Jörg Schek, Auteur ; F. Steidler, Auteur ; U. Schauer, Auteur Editeur : Munich : Bayerische Akademie der Wissenschaften Année de publication : 1977 Collection : DGK - A Sous-collection : Theoretische Geodäsie num. 087 Importance : 42 p. Format : 21 x 30 cm ISBN/ISSN/EAN : 978-3-7696-8171-0 Note générale : Bibliographie Langues : Allemand (ger) Descripteur : [Vedettes matières IGN] Triangulation [Termes IGN] compensation [Termes IGN] matrice creuse [Termes IGN] matrice de covariance [Termes IGN] réseau géodésique Index. décimale : 30.30 Triangulation - géodésie terrestre Résumé : (Auteur) The adjustment of large geodetic networks with distances and direction observations leads to large matrices of the normal equations, which generally are sparse, this means the share of- the nonzero elements is small. For the first time it is shown here that the factorization algorithms for general sparse matrices being scarcely considered in Geodesy, are suited very well for the solution of the occuring system of normal equations. Because of the non-linearity of this classical geodetic standard problem the application of the "four - step - factorization" will be discussed, consisting of the "optimal ordering", the symbolic factorization, the numeric factorization and the solution by "forward-backward substi-tution" . Furthermore, for the first time these modern methods are compared with classical iter-ative methods (method of conjugate gradients and successive overrelaxation). It has to be men-tioned here that with these iterative methods manipulations for acceleration of convergence, like scaling and nonlinearly regulated terminating criterion have been applied. With the aid of six geodetic networks of different size (50 - 2000 unknowns), which occur in geodetic reality these methods were tested in practice and the results compared. Two important observations are stressed especially: 1. Algorithms for the optimal ordering of the matrix of the normal equations (in other words for the optimal numbering of the nodes of the networks) are crucial. Quantitatively this can be proved by the reduction of calculation time from two hours to eleven seconds for the numeric factorization in the case of a network containing 2000 unknowns. Even with a matrix of the normal equations with a minimized bandwidth it could be proved in one case, that a simple ordering reduced also the time of factorization. 2. Iterative methods compare distinctly poor with direct methods. The SOR-method is only useful at homogeneous networks, where all points of the net which are connected by observations have the same distance (e.g. at triangulation networks). Although'the total number of the iter-ations of the method of conjugate gradients is surprisingly small, a distinctly superiority of the direct methods referring to the total calculation time of the solution of the adjust-ment problems is shown. This should be confirmed by the determination of selected elements of the covariance matrix for the error ellipses etc. Numéro de notice : 28228 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Monographie Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=63574

Exemplaires(1)

Code-barres	Cote	Support	Localisation	Section	Disponibilité
28228-01	30.30	Livre	Centre de documentation	En réserve M-103	Disponible