@misc{BreussCristianiDurouetal., author = {Breuß, Michael and Cristiani, Emiliano and Durou, Jean-Denis and Falcone, Maurizio and Vogel, Oliver}, title = {Perspective Shape from Shading: Ambiguity Analysis and Numerical Approximations}, series = {SIAM Journal on Imaging Sciences}, volume = {5}, journal = {SIAM Journal on Imaging Sciences}, number = {1}, issn = {1936-4954}, pages = {311 -- 342}, language = {en} } @inproceedings{WeickertHagenburgBreussetal., author = {Weickert, Joachim and Hagenburg, Kai Uwe and Breuß, Michael and Vogel, Oliver}, title = {Linear osmosis models for visual computing}, series = {Energy Minimization Methods in Computer Vision and Pattern Recognition, EMMCVPR 2013, Lund, Sweden, August 2013}, booktitle = {Energy Minimization Methods in Computer Vision and Pattern Recognition, EMMCVPR 2013, Lund, Sweden, August 2013}, editor = {Heyden, A. and Kahl, F. and Olsson, C. and Oskarsson, M. and Tai, X.-C.}, publisher = {Springer}, address = {Berlin}, isbn = {978-3-642-40394-1}, pages = {26 -- 39}, language = {en} } @misc{VogelHeuserBergerSchuetzetal., author = {Vogel-Heuser, Birgit and Berger, Ulrich and Sch{\"u}tz, Daniel and Sch{\"o}ler, Thorsten and Jeschke, Sabina and Ewert, Daniel and Niggemann, Oliver and Windmann, Stefan and Lehmann, Christian}, title = {Agentenbasierte Cyber-Physische Produktionssysteme: Anwendungen f{\"u}r die Industrie 4.0}, series = {atp-edition}, volume = {57}, journal = {atp-edition}, number = {9}, issn = {0178-2320}, pages = {36 -- 45}, language = {de} } @misc{BreussKemmVogel, author = {Breuß, Michael and Kemm, Friedemann and Vogel, Oliver}, title = {A numerical study of Newton interpolation with extremely high degrees}, series = {Kybernetika : international journal published by Institute of Information Theory and Automation}, volume = {54}, journal = {Kybernetika : international journal published by Institute of Information Theory and Automation}, number = {2}, issn = {0023-5954}, doi = {10.14736/kyb-2018-2-0279}, pages = {279 -- 288}, abstract = {In current textbooks the use of Chebyshev nodes with Newton interpolation is advocated as the most efficient numerical interpolation method in terms of approximation accuracy and computational effort. However, we show numerically that the approximation quality obtained by Newton interpolation with Fast Leja (FL) points is competitive to the use of Chebyshev nodes, even for extremely high degree interpolation. This is an experimental account of the analytic result that the limit distribution of FL points and Chebyshev nodes is the same when letting the number of points go to infinity. Since the FL construction is easy to perform and allows to add interpolation nodes on the fly in contrast to the use of Chebyshev nodes, our study suggests that Newton interpolation with FL points is currently the most efficient numerical technique for polynomial interpolation. Moreover, we give numerical evidence that any reasonable function can be approximated up to machine accuracy by Newton interpolation with FL points if desired, which shows the potential of this method.}, language = {en} }