TY - INPR A1 - Makhmudov, O. I. A1 - Niyozov, I. E. T1 - Regularization of the Cauchy Problem for the System of Elasticity Theory in R up (m) N2 - In this paper we consider the regularization of the Cauchy problem for a system of second order differential equations with constant coefficients. T3 - Preprint - (2005) 22 KW - the Cauchy problem KW - Lame system KW - elliptic system KW - ill-posed problem KW - Carleman matrix KW - regularization KW - Laplace equation Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-29983 ER - TY - JOUR A1 - Kirsche, Andreas A1 - Böckmann, Christine T1 - Pade iteration method for regularization JF - Applied mathematics and computation N2 - In this study we present iterative regularization methods using rational approximations, in particular, Pade approximants, which work well for ill-posed problems. We prove that the (k,j)-Pade method is a convergent and order optimal iterative regularization method in using the discrepancy principle of Morozov. Furthermore, we present a hybrid Pade method, compare it with other well-known methods and found that it is faster than the Landweber method. It is worth mentioning that this study is a completion of the paper [A. Kirsche, C. Bockmann, Rational approximations for ill-conditioned equation systems, Appl. Math. Comput. 171 (2005) 385-397] where this method was treated to solve ill-conditioned equation systems. (c) 2006 Elsevier Inc. All rights reserved. KW - Pade approximants KW - iterative regularization KW - ill-posed problem Y1 - 2006 U6 - https://doi.org/10.1016/j.amc.2006.01.011 SN - 0096-3003 VL - 180 IS - 2 SP - 648 EP - 663 PB - Elsevier CY - New York ER - TY - THES A1 - Helms, Andreas T1 - Anwendung des Mikrogravitationslinseneffekts zur Untersuchung astronomischer Objekte N2 - Die Untersuchung mikrogelinster astronomischer Objekte ermöglicht es, Informationen über die Größe und Struktur dieser Objekte zu erhalten. Im ersten Teil dieser Arbeit werden die Spektren von drei gelinsten Quasare, die mit dem Potsdamer Multi Aperture Spectrophotometer (PMAS) erhalten wurden, auf Anzeichen für Mikrolensing untersucht. In den Spektren des Vierfachquasares HE 0435-1223 und des Doppelquasares HE 0047-1756 konnten Hinweise für Mikrolensing gefunden werden, während der Doppelquasar UM 673 (Q 0142--100) keine Anzeichen für Mikrolensing zeigt. Die Invertierung der Lichtkurve eines Mikrolensing-Kausik-Crossing-Ereignisses ermöglicht es, das eindimensionale Helligkeitsprofil der gelinsten Quelle zu rekonstruieren. Dies wird im zweiten Teil dieser Arbeit untersucht. Die mathematische Beschreibung dieser Aufgabe führt zu einer Volterra'schen Integralgleichung der ersten Art, deren Lösung ein schlecht gestelltes Problem ist. Zu ihrer Lösung wird in dieser Arbeit ein lokales Regularisierungsverfahren angewendet, das an die kausale Strukture der Volterra'schen Gleichung besser angepasst ist als die bisher verwendete Tikhonov-Phillips-Regularisierung. Es zeigt sich, dass mit dieser Methode eine bessere Rekonstruktion kleinerer Strukturen in der Quelle möglich ist. Weiterhin wird die Anwendbarkeit der Regularisierungsmethode auf realistische Lichtkurven mit irregulärem Sampling bzw. größeren Lücken in den Datenpunkten untersucht. N2 - The study of microlensed astronomical objects can reveal information about the size and the structure of these objects. In the first part of this thesis we analyze the spectra of three lensed quasars obtained with the Potsdam Multi Aperture Spectrophotometer (PMAS). The spectra of the quadrupole quasar HE 0435--1223 and the double quasar HE 0047--1756 show evidence for microlensing whereas in the double quasar UM 673 (Q 0142--100) no evidence for microlensing could be found. By inverting the lightcurve of a microlensing caustic crossing event the one dimensional luminosity profile of the lensed source can be reconstructed. This is investigated in the second part of this thesis.The mathematical formulation of this problem leads to a Volterra integral equation of the first kind, whose solution is an ill-posed problem. For the solution we use a local regularization method which is better adapted to the causal structure of the Volterra integral equation compared to the so far used Tikhonov-Phillips regularization. Furthermore we show that this method is more robust on reconstructing small structures in the source profile. We also study the influence of irregular sampled data and gaps in the lightcurve on the result of the inversion. T2 - Anwendung des Mikrogravitationslinseneffekts zur Untersuchung astronomischer Objekte KW - Gravitationslinseneffekt KW - Mikrolensing KW - Quasar KW - Regularisierung KW - Schlecht gestelltes Problem KW - gravitational lensing KW - microlensing KW - quasar KW - regularization KW - ill-posed problem Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-0001532 ER - TY - INPR A1 - Böckmann, Christine A1 - Biele, Jens A1 - Neuber, Roland A1 - Niebsch, Jenny T1 - Retrieval of multimodal aerosol size distribution by inversion of multiwavelength data N2 - The ill-posed problem of aerosol size distribution determination from a small number of backscatter and extinction measurements was solved successfully with a mollifier method which is advantageous since the ill-posed part is performed on exactly given quantities, the points r where n(r) is evaluated may be freely selected. A new twodimensional model for the troposphere is proposed. T3 - NLD Preprints - 38 KW - Multiwavelength LIDAR KW - aerosol size distribution KW - ill-posed problem KW - inversion KW - mollifier method KW - coated and absorbing aerosols Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14360 ER -