Siegen Preprints on Geomathematics
Siegen Preprints on Geomathematics
The preprint series "Siegen Preprints on Geomathematics" was established in 2010. At present, the following preprints are available:
- P. Berkel, D. Fischer, V. Michel: Spline multiresolution and numerical results for joint gravitation and normal mode inversion with an outlook on sparse regularisation, 2010. The final publication is available at springerlink.com.
- M. Akram, V. Michel: Regularisation of the Helmholtz decomposition and its application to geomagnetic field modelling, 2010. The final publication is available at springerlink.com.
- V. Michel: Optimally localized approximate identities on the 2-sphere, 2010.
- N. Akhtar, V. Michel: Reproducing kernel based splines for the regularization of the inverse spheroidal gravimetric problem, 2011.
- D. Fischer, V. Michel: Sparse regularization of inverse gravimetry – case study: spatial and temporal mass variations in South America, 2011. The paper is published (in a revised version) in Inverse Problems 28 (2012), 065012 (34pp), click here for download.
- A.S. Fokas, O. Hauk, V. Michel: Electro-magneto-encephalography for the three-shell model: numerical implementation for distributed current in spherical geometry, 2011.
- M. Akram, I. Amna, V. Michel: A study of differential operators for complete orthonormal systems on a 3D ball, 2011.
- D. Fischer, V. Michel: How to combine spherical harmonics and localized bases for regional gravity modelling and inversion, 2012. The paper was accepted (in a revised version titled "Automatic best-basis selection for geophyiscal tomographic inverse problems") by Geophysical Journal International in 2013.
- D. Fischer, V. Michel: Inverting GRACE gravity data for local climate effects, 2012.
- V. Michel, R. Telschow: A non-linear approximation method on the sphere, 2014.
- V. Michel, R. Telschow: The regularized orthogonal functional matching pursuit for ill-posed inverse problems, 2014. The paper is published (in a revised version) in the SIAM Journal on Numerical Analysis, 54 (2016), 262-287.
- V. Michel, S. Orzlowski: On the null space of a class of Fredholm integral equations of the first kind, 2015.
- V. Michel, S. Orzlowski: On the convergence theorem for the Regularized Functional Matching Pursuit (RFMP) algorithm, 2016. The final publication is (soon) available at Springer, International Journal on Geomathematics.
- I. Amna, V. Michel: Pseudodifferential operators and equidistribution on the 3D-ball - an approach based on orthonormal basis systems, 2016. The paper is published (in a slightly revised version) in Numerical Functional Analysis and Optimization, 2017.
- S. Gramsch, M. Kontak, V. Michel: Three-dimensional simulation of nonwoven fabrics using a greedy approximation of the distribution of fiber directions, 2016.
- M. Gutting, B. Kretz, V. Michel, R. Telschow: Study on parameter choice methods for the RFMP with respect to downward continuation, 2016.
- V. Michel, S. Orzlowski, N. Schneider: Vectorial Slepian functions on the ball, 2017.
- V. Michel, F.J. Simons: A general approach to regularizing inverse problems with regional data using Slepian wavelets, 2017. This is an author-created, un-copyedited version of an article accepted for publication/published in "Inverse Problems". IOP Publishing Ltd. is not responsible for any errors or ommissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/1361-6420/aa9909 .
- M. Kontak, V. Michel: A greedy algorithm for non-linear inverse problems with an application to non-linear inverse gravimetry, 2018. Local download available: this is a post-peer-review, pre-copyedit version of an article published in GEM: International Journal on Geomathematics, topical collection "Mathematical Problems in Medical Imaging and Earth Sciences". The final authenticated version is available online at: https://link.springer.com/article/10.1007/s13137-018-0110-6.
- S. Leweke, V. Michel, A.S. Fokas: Electro-magnetoencephalography for the spherical multiple-shell model: novel integral operators with singular-value decompositions, 2018.
- V. Michel, N. Schneider: A first approach to learning a best basis for gravity field modelling, 2019.
- A. Ishtiaq, V. Michel, H.P. Scheffler: Theory of generalized discrepancies on a ball of arbitrary dimensions, 2019. For the revised and accepted paper, see this link to GEM: International Journal on Geomathematics.