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1	Transformation and approximation of rational Krylov spaces with an application to 2.5-dimensional direct current resistivity modeling Stein, Saskia 17 April 2021 (has links) Die vorliegende Arbeit befasst sich mit der Fragestellung, inwiefern sich gegebene Verfahren zur Approximation von rationalen Krylow-Räumen zur Berechnung von Matrixfunktionen eignen. Als Modellproblem wird dazu eine 2.5D-Formulierung eines Problems aus der Gleichstrom-Geoelektrik mit finiten Elementen formuliert und dann mittels Matrixfunktionen auf rationalen Krylow-Unterräumen gelöst. Ein weiterer Teil beschäftigt sich mit dem Vergleich zweier Verfahren zur Transformation bestehender rationaler Krylow-Räume. Bei beiden Varianten werden die zugrunde liegenden Pole getauscht ohne dass ein explizites Invertieren von Matrizen notwendig ist. In dieser Arbeit werden die über mehrere Publikationen verteilten Grundlagen einheitlich zusammengetragen und fehlende Zusammenhänge ergänzt. Beide Verfahren eignen sich prinzipiell um rationale Krylow-Räume zu approximieren. Dies wird anhand mehrerer Beispiele gezeigt. Anhand des Modellproblems werden Beschränkungen der Methoden verdeutlicht. info:eu-repo/classification/ddc/510 ddc:510 Krylov-Verfahren Matrixfunktion Ähnlichkeitstransformation Geophysik Prospektion Geoelektrische Widerstandsmethode Datenauswertung
2	Transformation model selection by multiple hypotheses testing Lehmann, Rüdiger 17 October 2016 (has links) (PDF) Transformations between different geodetic reference frames are often performed such that first the transformation parameters are determined from control points. If in the first place we do not know which of the numerous transformation models is appropriate then we can set up a multiple hypotheses test. The paper extends the common method of testing transformation parameters for significance, to the case that also constraints for such parameters are tested. This provides more flexibility when setting up such a test. One can formulate a general model with a maximum number of transformation parameters and specialize it by adding constraints to those parameters, which need to be tested. The proper test statistic in a multiple test is shown to be either the extreme normalized or the extreme studentized Lagrange multiplier. They are shown to perform superior to the more intuitive test statistics derived from misclosures. It is shown how model selection by multiple hypotheses testing relates to the use of information criteria like AICc and Mallows’ Cp, which are based on an information theoretic approach. Nevertheless, whenever comparable, the results of an exemplary computation almost coincide. Koordinatentransformation Hypothesentest Affintransformation Ähnlichkeitstransformation Gauß-Markow-Model mit Nebenbedingungen Normierter Lagrange-Multiplikator Studentisierter Lagrange-Multiplikator Akaike's Informationskriterium Mallows’ Cp Coordinate transformation Hypothesis test Affine transformation Similarity transformation Gauss-Markov model with constraints Normalized Lagrange multiplier Studentized Lagrange multiplier Akaike information criterion Mallows’ Cp ddc:500 rvk:ZI 9070
3	Transformation model selection by multiple hypotheses testing Lehmann, Rüdiger January 2014 (has links) Transformations between different geodetic reference frames are often performed such that first the transformation parameters are determined from control points. If in the first place we do not know which of the numerous transformation models is appropriate then we can set up a multiple hypotheses test. The paper extends the common method of testing transformation parameters for significance, to the case that also constraints for such parameters are tested. This provides more flexibility when setting up such a test. One can formulate a general model with a maximum number of transformation parameters and specialize it by adding constraints to those parameters, which need to be tested. The proper test statistic in a multiple test is shown to be either the extreme normalized or the extreme studentized Lagrange multiplier. They are shown to perform superior to the more intuitive test statistics derived from misclosures. It is shown how model selection by multiple hypotheses testing relates to the use of information criteria like AICc and Mallows’ Cp, which are based on an information theoretic approach. Nevertheless, whenever comparable, the results of an exemplary computation almost coincide. info:eu-repo/classification/ddc/500 ddc:500

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