TY - GEN A1 - Breuß, Michael A1 - Cristiani, Emiliano A1 - Durou, Jean-Denis A1 - Falcone, Maurizio A1 - Vogel, Oliver T1 - Perspective Shape from Shading: Ambiguity Analysis and Numerical Approximations T2 - SIAM Journal on Imaging Sciences Y1 - 2012 SN - 1936-4954 VL - 5 IS - 1 SP - 311 EP - 342 ER - TY - CHAP A1 - Weickert, Joachim A1 - Hagenburg, Kai Uwe A1 - Breuß, Michael A1 - Vogel, Oliver ED - Heyden, A. ED - Kahl, F. ED - Olsson, C. ED - Oskarsson, M. ED - Tai, X.-C. T1 - Linear osmosis models for visual computing T2 - Energy Minimization Methods in Computer Vision and Pattern Recognition, EMMCVPR 2013, Lund, Sweden, August 2013 Y1 - 2013 SN - 978-3-642-40394-1 SN - 978-3-642-40395-8 SP - 26 EP - 39 PB - Springer CY - Berlin ER - TY - GEN A1 - Vogel-Heuser, Birgit A1 - Berger, Ulrich A1 - Schütz, Daniel A1 - Schöler, Thorsten A1 - Jeschke, Sabina A1 - Ewert, Daniel A1 - Niggemann, Oliver A1 - Windmann, Stefan A1 - Lehmann, Christian T1 - Agentenbasierte Cyber-Physische Produktionssysteme: Anwendungen für die Industrie 4.0 T2 - atp-edition Y1 - 2015 SN - 0178-2320 SN - 2190-4111 VL - 57 IS - 9 SP - 36 EP - 45 ER - TY - GEN A1 - Breuß, Michael A1 - Kemm, Friedemann A1 - Vogel, Oliver T1 - A numerical study of Newton interpolation with extremely high degrees T2 - Kybernetika : international journal published by Institute of Information Theory and Automation N2 - 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. KW - polynomial interpolation KW - Newton interpolation KW - interpolation nodes KW - Chebyshev nodes KW - Leja ordering KW - fast Leja points Y1 - 2018 U6 - https://doi.org/10.14736/kyb-2018-2-0279 SN - 0023-5954 VL - 54 IS - 2 SP - 279 EP - 288 ER -