Thèses : « Inverses Problem; Regularisierung »

1

Bonesky, Thomas. « Regularization of inverse problems and inexact operator evaluations ». Berlin Logos-Verl, 2009. http://d-nb.info/997726814/04.

Texte intégral

Styles APA, Harvard, Vancouver, ISO, etc.

2

Trede, Dennis. « Inverse problems with sparsity constraints convergence rates and exact recovery ». Berlin Logos-Verl, 2010. http://d-nb.info/1002361532/04.

Texte intégral

Styles APA, Harvard, Vancouver, ISO, etc.

3

Flemming, Jens. « Quadratic Inverse Problems and Sparsity Promoting Regularization ». Doctoral thesis, Universitätsbibliothek Chemnitz, 2018. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-232402.

Texte intégral

Résumé :

Ill-posed inverse problems with quadratic structure are introduced, studied and solved. As an example an inverse problem appearing in laser optics is solved numerically based on a new regularized inversion algorithm. In addition, the theory of sparsity promoting regularization is extended to situations in which sparsity cannot be expected and also to equations with non-injective operators.

Styles APA, Harvard, Vancouver, ISO, etc.

4

Freitag, Melina. « On the Influence of Multiplication Operators on the Ill-posedness of Inverse Problems ». Master's thesis, Universitätsbibliothek Chemnitz, 2004. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200401504.

Texte intégral

Résumé :

In this thesis we deal with the degree of ill-posedness of linear operator equations in Hilbert spaces, where the operator may be decomposed into a compact linear integral operator with a well-known decay rate of singular values and a multiplication operator. This case occurs for example for nonlinear operator equations, where the local degree of ill-posedness is investigated via the Frechet derivative. If the multiplier function has got zeroes, the determination of the local degree of ill-posedness is not trivial. We are going to investigate this situation, provide analytical tools as well as their limitations. By using several numerical approaches for computing the singular values of the operator we find that the degree of ill-posedness does not change through those multiplication operators. We even provide a conjecture, verified by several numerical studies, how these multiplication operators influence the singular values of the operator equation. Finally we analyze the influence of those multiplication operators on the opportunities of Tikhonov regularization and corresponding convergence rates. In this context we also provide a short summary on the relationship between nonlinear problems and their linearizations
Diese Arbeit beschaeftigt sich mit dem Grad der Inkorrektheit linearer Operatorgleichungen in Hilbertraeumen, die sich als Komposition eines vollstetigen linearen Integraloperators mit bekannter Abklingrate der Singulaerwerte und eines Multiplikationsoperators darstellen lassen. Dieser Fall tritt beispielsweise bei nichtlinearen Operatorgleichungen auf, wobei der lokale Inkorrektheitsgrad ueber die Frechetableitung bestimmt wird. Falls die Multiplikatorfunktion Nullstellen hat, so ist die Bestimmung des lokalen Grades der Inkorrektheit nicht einfach. Moeglichkeiten und Grenzen der Analysis fuer diese Situation werden betrachtet. Unterschiedliche numerische Ansaetze fuer die Bestimmung der Singulaerwerte liefern, dass der Grad der Inkorrektheit durch die Multiplikationsoperatoren nicht veraendert wird. Es wird sogar ein Zusammenhang angegeben, wie Multiplikationsoperatoren die Singulaerwerte beeinflussen. Schliesslich werden Moeglichkeiten der Tikhonov-Regularisierung unter Einfluss der Multiplikationsoperatoren untersucht. In diesem Zusammenhang wird auch eine kurze Zusammenfassung zur Beziehung von nichtlinearen Problemen und ihren Linearisierungen gegeben

Styles APA, Harvard, Vancouver, ISO, etc.

5

Krämer, Romy, Matthias Richter et Bernd Hofmann. « Parameter estimation in a generalized bivariate Ornstein-Uhlenbeck model ». Universitätsbibliothek Chemnitz, 2005. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200501307.

Texte intégral

Résumé :

In this paper, we consider the inverse problem of calibrating a generalization of the bivariate Ornstein-Uhlenbeck model introduced by Lo and Wang. Even though the generalized Black-Scholes option pricing formula still holds, option prices change in comparison to the classical Black-Scholes model. The time-dependent volatility function and the other (real-valued) parameters in the model are calibrated simultaneously from option price data and from some empirical moments of the logarithmic returns. This gives an ill-posed inverse problem, which requires a regularization approach. Applying the theory of Engl, Hanke and Neubauer concerning Tikhonov regularization we show convergence of the regularized solution to the true data and study the form of source conditions which ensure convergence rates.

Styles APA, Harvard, Vancouver, ISO, etc.

6

Hein, Torsten. « On solving implicitly defined inverse problems by SQP-approaches ». Universitätsbibliothek Chemnitz, 2007. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200702148.

Texte intégral

Résumé :

In this paper two basic SQP-approaches for solving implicitly defined inverse problems are presented. Such problems often arises in parameter identification for differential equations. We also include regularization strategies which differ from similar problems in Optimal control. The main focus is on formulating saddle point problems for calculating the next iterate. Conditions for the unique and stable solvability of these problems are presented. The analytical considerations are illustrated by two examples including their discretizations and a numerical case study.

Styles APA, Harvard, Vancouver, ISO, etc.

7

Hein, Torsten. « Analytische und numerische Studien zu inversen Problemen der Optionspreisbildung ». Doctoral thesis, [S.l. : s.n.], 2003. http://deposit.ddb.de/cgi-bin/dokserv?idn=969860986.

Texte intégral

Styles APA, Harvard, Vancouver, ISO, etc.

8

Anzengruber, Stephan W., Bernd Hofmann et Peter Mathé. « Regularization properties of the discrepancy principle for Tikhonov regularization in Banach spaces ». Universitätsbibliothek Chemnitz, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-99353.

Texte intégral

Résumé :

The stable solution of ill-posed non-linear operator equations in Banach space requires regularization. One important approach is based on Tikhonov regularization, in which case a one-parameter family of regularized solutions is obtained. It is crucial to choose the parameter appropriately. Here, a variant of the discrepancy principle is analyzed. In many cases such parameter choice exhibits the feature, called regularization property below, that the chosen parameter tends to zero as the noise tends to zero, but slower than the noise level. Here we shall show such regularization property under two natural assumptions. First, exact penalization must be excluded, and secondly, the discrepancy principle must stop after a finite number of iterations. We conclude this study with a discussion of some consequences for convergence rates obtained by the discrepancy principle under the validity of some kind of variational inequality, a recent tool for the analysis of inverse problems.

Styles APA, Harvard, Vancouver, ISO, etc.

9

Shao, Yuanyuan. « Beiträge zur Regularisierung inverser Probleme und zur bedingten Stabilität bei partiellen Differentialgleichungen ». Doctoral thesis, Universitätsbibliothek Chemnitz, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-102801.

Texte intégral

Résumé :

Wir betrachten die lineare inverse Probleme mit gestörter rechter Seite und gestörtem Operator in Hilberträumen, die inkorrekt sind. Um die Auswirkung der Inkorrektheit zu verringen, müssen spezielle Lösungsmethode angewendet werden, hier nutzen wir die sogenannte Tikhonov Regularisierungsmethode. Die Regularisierungsparameter wählen wir aus das verallgemeinerte Defektprinzip. Eine typische numerische Methode zur Lösen der nichtlinearen äquivalenten Defektgleichung ist Newtonverfahren. Wir schreiben einen Algorithmus, die global und monoton konvergent für beliebige Startwerte garantiert. Um die Stabilität zu garantieren, benutzen wir die Glattheit der Lösung, dann erhalten wir eine sogenannte bedingte Stabilität. Wir demonstrieren die sogenannte Interpolationsmethode zur Herleitung von bedingten Stabilitätsabschätzungen bei inversen Problemen für partielle Differentialgleichungen.

Styles APA, Harvard, Vancouver, ISO, etc.

10

Bürger, Steven, et Bernd Hofmann. « About a deficit in low order convergence rates on the example of autoconvolution ». Universitätsbibliothek Chemnitz, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-130630.

Texte intégral

Résumé :

We revisit in L2-spaces the autoconvolution equation x ∗ x = y with solutions which are real-valued or complex-valued functions x(t) defined on a finite real interval, say t ∈ [0,1]. Such operator equations of quadratic type occur in physics of spectra, in optics and in stochastics, often as part of a more complex task. Because of their weak nonlinearity deautoconvolution problems are not seen as difficult and hence little attention is paid to them wrongly. In this paper, we will indicate on the example of autoconvolution a deficit in low order convergence rates for regularized solutions of nonlinear ill-posed operator equations F(x)=y with solutions x† in a Hilbert space setting. So for the real-valued version of the deautoconvolution problem, which is locally ill-posed everywhere, the classical convergence rate theory developed for the Tikhonov regularization of nonlinear ill-posed problems reaches its limits if standard source conditions using the range of F (x† )∗ fail. On the other hand, convergence rate results based on Hölder source conditions with small Hölder exponent and logarithmic source conditions or on the method of approximate source conditions are not applicable since qualified nonlinearity conditions are required which cannot be shown for the autoconvolution case according to current knowledge. We also discuss the complex-valued version of autoconvolution with full data on [0,2] and see that ill-posedness must be expected if unbounded amplitude functions are admissible. As a new detail, we present situations of local well-posedness if the domain of the autoconvolution operator is restricted to complex L2-functions with a fixed and uniformly bounded modulus function.

Styles APA, Harvard, Vancouver, ISO, etc.

11

Rückert, Nadja. « Studies on two specific inverse problems from imaging and finance ». Doctoral thesis, Universitätsbibliothek Chemnitz, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-91587.

Texte intégral

Résumé :

This thesis deals with regularization parameter selection methods in the context of Tikhonov-type regularization with Poisson distributed data, in particular the reconstruction of images, as well as with the identiﬁcation of the volatility surface from observed option prices. In Part I we examine the choice of the regularization parameter when reconstructing an image, which is disturbed by Poisson noise, with Tikhonov-type regularization. This type of regularization is a generalization of the classical Tikhonov regularization in the Banach space setting and often called variational regularization. After a general consideration of Tikhonov-type regularization for data corrupted by Poisson noise, we examine the methods for choosing the regularization parameter numerically on the basis of two test images and real PET data. In Part II we consider the estimation of the volatility function from observed call option prices with the explicit formula which has been derived by Dupire using the Black-Scholes partial diﬀerential equation. The option prices are only available as discrete noisy observations so that the main diﬃculty is the ill-posedness of the numerical diﬀerentiation. Finite diﬀerence schemes, as regularization by discretization of the inverse and ill-posed problem, do not overcome these diﬃculties when they are used to evaluate the partial derivatives. Therefore we construct an alternative algorithm based on the weak formulation of the dual Black-Scholes partial diﬀerential equation and evaluate the performance of the ﬁnite diﬀerence schemes and the new algorithm for synthetic and real option prices.

Styles APA, Harvard, Vancouver, ISO, etc.

12

Shao, Yuanyuan [Verfasser], Bernd [Akademischer Betreuer] Hofmann, Bernd [Gutachter] Hofmann, Ulrich [Akademischer Betreuer] Tautenhahn, Ljudmila [Akademischer Betreuer] Bordag et Barbara [Gutachter] Kaltenbacher. « Beiträge zur Regularisierung inverser Probleme und zur bedingten Stabilität bei partiellen Differentialgleichungen / Yuanyuan Shao ; Gutachter : Bernd Hofmann, Barbara Kaltenbacher ; Bernd Hofmann, Ulrich Tautenhahn, Ljudmila Bordag ». Chemnitz : Universitätsbibliothek Chemnitz, 2013. http://d-nb.info/1214244815/34.

Texte intégral

Styles APA, Harvard, Vancouver, ISO, etc.

13

Flemming, Jens. « Quadratic Inverse Problems and Sparsity Promoting Regularization : Two subjects, some links between them, and an application in laser optics ». Doctoral thesis, 2017. https://monarch.qucosa.de/id/qucosa%3A20855.

Texte intégral

Résumé :

Ill-posed inverse problems with quadratic structure are introduced, studied and solved. As an example an inverse problem appearing in laser optics is solved numerically based on a new regularized inversion algorithm. In addition, the theory of sparsity promoting regularization is extended to situations in which sparsity cannot be expected and also to equations with non-injective operators.

Styles APA, Harvard, Vancouver, ISO, etc.

14

Schmitt, Uwe [Verfasser]. « Effiziente Verfahren zur Regularisierung dynamischer inverser Probleme / von Uwe Schmitt ». 2001. http://d-nb.info/1006761195/34.

Texte intégral

Styles APA, Harvard, Vancouver, ISO, etc.

15

Shao, Yuanyuan. « Beiträge zur Regularisierung inverser Probleme und zur bedingten Stabilität bei partiellen Differentialgleichungen ». Doctoral thesis, 2012. https://monarch.qucosa.de/id/qucosa%3A19827.

Texte intégral

Résumé :

Wir betrachten die lineare inverse Probleme mit gestörter rechter Seite und gestörtem Operator in Hilberträumen, die inkorrekt sind. Um die Auswirkung der Inkorrektheit zu verringen, müssen spezielle Lösungsmethode angewendet werden, hier nutzen wir die sogenannte Tikhonov Regularisierungsmethode. Die Regularisierungsparameter wählen wir aus das verallgemeinerte Defektprinzip. Eine typische numerische Methode zur Lösen der nichtlinearen äquivalenten Defektgleichung ist Newtonverfahren. Wir schreiben einen Algorithmus, die global und monoton konvergent für beliebige Startwerte garantiert. Um die Stabilität zu garantieren, benutzen wir die Glattheit der Lösung, dann erhalten wir eine sogenannte bedingte Stabilität. Wir demonstrieren die sogenannte Interpolationsmethode zur Herleitung von bedingten Stabilitätsabschätzungen bei inversen Problemen für partielle Differentialgleichungen.

Styles APA, Harvard, Vancouver, ISO, etc.

16

Frick, Sophie. « Change point estimation in noisy Hammerstein integral equations ». Doctoral thesis, 2010. http://hdl.handle.net/11858/00-1735-0000-0006-B6A4-4.

Texte intégral

Styles APA, Harvard, Vancouver, ISO, etc.

Thèses sur le sujet « Inverses Problem; Regularisierung »

Créez une référence correcte selon les styles APA, MLA, Chicago, Harvard et plusieurs autres