**Operator differential-algebraic equations with noise arising in fluid dynamics**

*Altmann, Robert ; Levajković, Tijana ; Mena, Hermann* (2016)

We study linear semi-explicit stochastic operator differential algebraic equations (DAEs) for which the constraint equation is given in an explicit form. In particular, this includes the Stokes equations arising in fluid dynamics. We combine a white noise polynomial chaos expansion approach to include stochastic perturbations with deterministic regularization techniques. With this, we are able ...

**Backward error analysis of the shift-and-invert Arnoldi algorithm**

*Schröder, Christian ; Taslaman, Leo* (2015)

We perform a backward error analysis of the inexact shift-and-invert Arnoldi algorithm. We consider inexactness in the solution of the arising linear systems, as well as in the orthonormalization steps, and take the non-orthonormality of the computed Krylov basis into account. We show that the computed basis and Hessenberg matrix satisfy an exact shift-and-invert Krylov relation for a perturbed...

**Simulation of multibody systems with servo constraints through optimal control**

*Altmann, Robert ; Heiland, Jan* (2016)

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**Wavelet methods for a weighted sparsity penalty for region of interest tomography**

*Klann, Esther ; Quinto, Eric Todd ; Ramlau, Ronny* (2015)

We consider region of interest (ROI) tomography of piecewise constant functions. Additionally, an algorithm is developed for ROI tomography of piecewise constant functions using a Haar wavelet basis. A weighted ℓp–penalty is used with weights that depend on the relative location of wavelets to the region of interest. We prove that the proposed method is a regularization method, i.e., that the r...

**Regularization properties of Mumford–Shah-type functionals with perimeter and norm constraints for linear ill-posed problems**

*Klann, Esther ; Ramlau, Ronny* (2013)

In this paper we consider the simultaneous reconstruction and segmentation of a function f from measurements g = Kf, where K is a linear operator. Assuming that the inversion of K is illposed, regularization methods have to be used for the inversion process in case of inexact data. We propose using a Mumford–Shah-type functional for the stabilization of the inversion. Restricting our analysis t...

**A Mumford–Shah-type approach to simultaneous reconstruction and segmentation for emission tomography problems with Poisson statistics**

*Klann, Esther ; Ramlau, Ronny ; Sun, Peng* (2017)

We propose a variational model to simultaneous reconstruction and segmentation in emission tomography. As in the original Mumford–Shah model [27] we use the contour length as penalty term to preserve edge information whereas a different data fidelity term is used to measure the information discrimination between the computed tomography data of the reconstructed object and the observed (or simul...