TY - JOUR A1 - Ebner, Andrea A1 - Frikel, Jürgen A1 - Lorenz, D. A1 - Schwab, J. A1 - Haltmeier, Markus T1 - Regularization of inverse problems by filtered diagonal frame decomposition JF - Applied and Computational Harmonic Analysis N2 - Inverse problems are at the heart of many practical problems such as image reconstruction or nondestructive testing. A characteristic feature is their instability with respect to data perturbations. To stabilize the inversion process, regularization methods must be developed and applied. In this paper, we introduce the concept of filtered diagonal frame decomposition, which extends the classical filtered SVD to the case of frames. The use of frames as generalized singular systems allows a better match to a given class of potential solutions and is also beneficial for problems where the SVD is not analytically available. We show that filtered diagonal frame decompositions yield convergent regularization methods, derive convergence rates under source conditions and prove order optimality. Our analysis applies to bounded and unbounded forward operators. As a practical application of our tools, we study filtered diagonal frame decompositions for inverting the Radon transform as an unbounded operator on L2(R2). Y1 - 2023 U6 - https://doi.org/10.1016/j.acha.2022.08.005 N1 - Preprint unter: https://arxiv.org/pdf/2008.06219.pdf OPUS-Einrag unter: https://opus4.kobv.de/opus4-oth-regensburg/admin/document/edit/id/2290 VL - 62 IS - January SP - 66 EP - 83 PB - Elsevier ER - TY - JOUR A1 - Bruni, S. A1 - Meijaard, J. P. A1 - Rill, Georg A1 - Schwab, A. L. T1 - State-of-the-art and challenges of railway and road vehicle dynamics with multibody dynamics approaches JF - Multibody System Dynamics N2 - A review of the current use of multibody dynamics methods in the analysis of the dynamics of vehicles is given. Railway vehicle dynamics as well as road vehicle dynamics are considered, where for the latter the dynamics of cars and trucks and the dynamics of single-track vehicles, in particular motorcycles and bicycles, are reviewed. Commonalities and differences are shown, and open questions and challenges are given as directions for further research in this field. KW - AUTOMATIC-GENERATION KW - BICYCLE DYNAMICS KW - Bicycles KW - CREEP FORCES KW - FREIGHT WAGON KW - LATERAL DYNAMICS KW - LINEAR-MODEL KW - Motorcycles KW - NON-HERTZIAN KW - PASSIVE RIDER KW - Railway vehicles KW - Review KW - Road vehicles KW - ROLLING-CONTACT KW - vehicle dynamics KW - WHEELSET-TRACK INTERACTION Y1 - 2020 U6 - https://doi.org/10.1007/s11044-020-09735-z VL - 49 IS - 1 SP - 1 EP - 32 PB - Springer ER -