Prof. Dr. Martin Buhmann
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Professur für Numerik Heinrich-Buff-Ring 44
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Sprechstunde: nach Vereinbarung
Arbeitsgruppe: Numerische Mathematik
Bachelor-Arbeiten: werden in vielen Teilgebieten der Numerik vergeben, z. B. in Optimierung und Approximationstheorie im weitesten Sinne.
- Mathematikum/Mathematics Science Centre
- Jahr der Mathematik
- stellv. Sprecher der Konferenz der mathematischen Fachbereiche
- Europabeauftragter/Information for studying abroad
Derzeitige Forschungsschwerpunkte (Current Research)
- Approximationseigenschaften Radialer Basisfunktionen
- Neuronale Netze und Ridge-Funktionen
- Wavelets
Internationale Kontakte (Current International Contacts)
- University of Cambridge
- CityUniversity, Hong Kong
- University of Canterbury, Christchurch, New Zealand
- Technion Haifa
- University of Wisconsin-Madison
- Jagiellonische Universität Krakau (Polen)
- University of Granada, Spain
- Jaen University Spain
- Tel Aviv University
- Editorial Board, Journal of Approximation Theory
- Editorial Board, Jaen Journal on Approximation (Managing Editor)
- Editorial Board, Numerical Algorithms
- Oberwolfach ...and nearby Oberwolfach in the Black Forest: Brown Bears! And here are two (Quelle Stiftung für Bären):
Einige meiner Veröffentlichungen (Some of my papers)
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Strictly positive definite kernels on the 2-sphere: from radial symmetry to eigenvalue block structure, mit Janin Jäger IMA Journal of Numerical Analysis, https://doi.org/10.1093/imanum/drab012
Published: 03 May 2021 - Discretization of high-dimensional domains, mit F. Dai, Y. Niu, Advances in Mathematics, 381 (2021).
- Analysis of a new class of rational RBF expansions, mit S. DeMarchi, E. Perracchione, IMA Journal of Numerical Analysis 40 (2020), 1972–1993.
- Implementing and modifying Broyden class up- dates for large scale optimization, mit D. Siegel, Computational Optimization and Applications 78 (2021), 181–203.
- Pólya type criteria for conditional strict positive definiteness of functions on spheres, mit J. Jäger, Journal of Approximation Theory 257 (2020).
- Multiply monotone functions for radial basis function interpolation: extensions and new kernels, mit J. Jäger, Journal of Approximation Theory 256 (2020).
- Radial discrete PDE splines on Lipschitz domains, mit J. Jodar, M. Rodriguez, J. Math. Anal. Applic. 479 (1), 2019, 214–241.
- Radial basis functions with compact support for multivariate geostatistics, mit E. Porcu, D. Daley, M. Bevilacqua, Stochastic environmental research and risk assessment 27 (4) 2013, 909-922.
- Radial basis functions, Encyclopedia of computational and applied mathematics, B. Enquist, ed., Springer, 2016.
- Radial basis function networks, Encyclopedia of Machine Learning and Data Mining, C. Sammut and G.I. Webb, eds., 2016.
- Pointwise approximation with quasi-interpolation by radial basis functions, mit Feng Dai, Journal of Approximation Theory 192, 2015, 156-192.
- Compression using quasi-interpolation, mit Feng Dai, Jaen Journal on Approximation 7, 2015, 203-230.
- On the convergence of cardinal interpolation by parametrized radial basis functions, mit Han Feng, Journal of Mathematical Analysis and Applications, to appear.
- Reconstruction if EEG data using radial basis functions, mit Janin Jäger, A. Klein und W. Skrandies, Electroencephalography and Clinical Neurophysiology 127, 2016, 1978-1983
- Professor M J D Powell (1936-2015), IMA Mathematics today, August 2015.
- A note on radial basis function interpolation limits, mit S. Dinew und E. Larsson, IMA Journal of Numerical Analysis 30, 543-554, 2010
- Limits of radial basis function interpolants, mit S. Dinew, Communications in Pure and Applied Analysis 6, 569 - 585, 2007
- Cubic spline prewavelets on the four direction mesh, mit O. Davydov und T. N. T. Goodman, Foundations of Computational Mathematics 3, 113 - 133, 2003
- A view on spline prewavelets, mit D. F. Griffiths und G. A. Watson, Proceedings of the 20th Dundee Biennial Numerical Analysis Conference, erschienen in dem University of Dundee Report NA/217, 23 - 27, 2003
- Sobolev-orthogonal functions an spectral methods, mit A. Iserles und S. P. Anderson, Proceedings of the Algorithms for Approximation 4 Conference, Charlesworth Publ. Huddersfield, 198 - 211, 2002
- Box-spline prewavelets with small support, mit O. Davydov und T. N. T. Goodman, J.Approximation Theory 112, 16 - 27, 2001
- A new class of radial basis functions with compact support, Mathematics of Computation 70, 307 - 318, 2001
- Radial basis functions: the state-of-the-art and new results, Acta Numerica 9, 1 - 37, 2000
- Identifying Linear Combinations of Ridge Functions, mit A. Pinkus, Advances in Applied Mathematics 22, Seiten 103 - 118, 1999
- Radial Functions on Compact Support, Proceedings of the Edingburgh Mathematical Society 41, 33 - 46, 1998
- Neue und alte Thesen über Wavelets, Elemente der Mathematik 51, 145 - 155, 1996
- On a recovery problem, mit A. Pinkus, Annals of Numerical Mathematics 4, 129 - 142, 1996
- Multiquadric Pre-Wavelets on Non-Equally Spaced Knots in One Dimension, Mathematics of Computation 64, 1611 - 1625, 1995