Inhaltspezifische Aktionen

Prof. Dr. Martin Buhmann

Professur für Numerik

Heinrich-Buff-Ring 44
35392 Gießen
HRZ, Raum 119

 

 

Sprechstunde: nach Vereinbarung

Arbeitsgruppe: Numerische Mathematik

Bachelor-Arbeiten: werden in vielen Teilgebieten der Numerik vergeben, z. B. in Optimierung und Approximationstheorie im weitesten Sinne.

 

 

Derzeitige Forschungsschwerpunkte (Current Research)

  1. Approximationseigenschaften Radialer Basisfunktionen
  2. Neuronale Netze und Ridge-Funktionen
  3. Wavelets   

Internationale Kontakte (Current International Contacts)

  1. University of Cambridge
  2. CityUniversity, Hong Kong
  3. University of Canterbury, Christchurch, New Zealand
  4. Technion Haifa
  5. University of Wisconsin-Madison
  6. Jagiellonische Universität Krakau (Polen)
  7. University of Granada, Spain
  8. Jaen University Spain
  9. Tel Aviv University
  10. Editorial Board, Journal of Approximation  Theory
  11. Editorial Board, Jaen Journal on Approximation (Managing Editor)
  12. Editorial Board, Numerical Algorithms
  13. Oberwolfach ...and nearby Oberwolfach in the Black Forest: Brown Bears!  And here are two (Quelle Stiftung für Bären):

 Buhmann Vortrag

Einige meiner Veröffentlichungen (Some of my papers)

 

  1. 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
  2. Discretization of high-dimensional domains, mit F. Dai, Y. Niu, Advances in Mathematics, 381 (2021).
  3. Analysis of a new class of rational RBF expansions, mit S. DeMarchi, E. Perracchione, IMA Journal of Numerical Analysis 40 (2020), 1972–1993.
  4. Implementing and modifying Broyden class up- dates for large scale optimization, mit D. Siegel, Computational Optimization and Applications 78 (2021), 181–203.
  5. Pólya type criteria for conditional strict positive definiteness of functions on spheres, mit J. Jäger, Journal of Approximation Theory 257 (2020).
  6. Multiply monotone functions for radial basis function interpolation: extensions and new kernels, mit J. Jäger, Journal of Approximation Theory 256 (2020).
  7. Radial discrete PDE splines on Lipschitz domains, mit J. Jodar, M. Rodriguez, J. Math. Anal. Applic. 479 (1), 2019, 214–241.
  8. 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.
  9. Radial basis functions, Encyclopedia of computational and applied mathematics, B. Enquist, ed., Springer, 2016.
  10. Radial basis function networks, Encyclopedia of Machine Learning and Data Mining, C. Sammut and G.I. Webb, eds., 2016.
  11. Pointwise approximation with quasi-interpolation by radial basis functions, mit Feng Dai, Journal of Approximation Theory 192, 2015, 156-192.
  12. Compression using quasi-interpolation, mit Feng Dai, Jaen Journal on Approximation 7, 2015, 203-230.
  13. On the convergence of cardinal interpolation by parametrized radial basis functions,  mit Han Feng, Journal of Mathematical Analysis and Applications, to appear.
  14. Reconstruction if EEG data using radial basis functions, mit Janin Jäger, A. Klein und W. Skrandies, Electroencephalography and Clinical Neurophysiology 127, 2016, 1978-1983
  15. Professor M J D Powell (1936-2015), IMA Mathematics today, August 2015.
  16. A note on radial basis function interpolation limits, mit S. Dinew und E. Larsson, IMA Journal of Numerical Analysis 30, 543-554, 2010
  17. Limits of radial basis function interpolants, mit S. Dinew, Communications in Pure and Applied Analysis 6, 569 - 585, 2007
  18. Cubic spline prewavelets on the four direction mesh, mit O. Davydov und T. N. T. Goodman,  Foundations of Computational Mathematics 3, 113 - 133, 2003
  19. 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
  20. 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
  21. Box-spline prewavelets with small support, mit O. Davydov und T. N. T. Goodman, J.Approximation Theory 112, 16 - 27, 2001
  22. A new class of radial basis functions with compact support, Mathematics of Computation 70, 307 - 318, 2001
  23. Radial basis functions: the state-of-the-art and new results, Acta Numerica 9, 1 - 37, 2000
  24. Identifying Linear Combinations of Ridge Functions, mit A. Pinkus, Advances in Applied Mathematics 22, Seiten 103 - 118, 1999
  25. Radial Functions on Compact Support, Proceedings of the Edingburgh Mathematical Society 41, 33 - 46, 1998
  26. Neue und alte Thesen über Wavelets, Elemente der Mathematik 51, 145 - 155, 1996
  27. On a recovery problem, mit A. Pinkus, Annals of Numerical Mathematics 4, 129 - 142, 1996
  28. Multiquadric Pre-Wavelets on Non-Equally Spaced Knots in One Dimension, Mathematics of Computation 64, 1611 - 1625, 1995