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DTSTART:19810329T020000
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BEGIN:VEVENT
UID:news1538@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20230915T113109
DTSTART;TZID=Europe/Zurich:20230929T110000
SUMMARY:Seminar in Numerical Analysis: Rüdiger Kempf (U Bayreuth)
DESCRIPTION:Reproducing kernel Hilbert spaces (RKHSs) and the closely rela
 ted kernel methods are well-established and well-studied tools in classi
 cal approximation theory. More recently\, they see many uses in other prob
 lems in applied and numerical analysis.\\r\\nIn machine learning\, support
  vector machines heavily rely on RKHSs. For neural networks Barron spaces 
 are connected to certain RKHSs and offer a possibility for a theoretical a
 nalysis of these networks.\\r\\nAnother application of RKHSs is in high(er
 )-dimensional approximation. For instance in the field of quasi Monte-Carl
 o methods\, kernel-techniques are used to derive an error analysis for hig
 h-dimensional quadrature rules. We also developed a novel kernel-based app
 roximation method for higher-dimensional meshfree function reconstruction\
 , based on Smolyak operators.\\r\\nIn this talk I will provide an introduc
 tion into the theory of RKHSs\, their kernels and associated kernel method
 s. In particular\, I will focus on a multiscale approximation scheme for r
 escaled radial basis functions. This method will then be used to derive th
 e new tensor product multilevel method for higher- dimensional meshfree 
 approximation\, which I will discuss in detail.\\r\\n\\r\\nFor further inf
 ormation about the seminar\, please visit this webpage [t3://page?uid=1115
 ].
X-ALT-DESC:<p>Reproducing kernel Hilbert spaces (RKHSs)&nbsp\;and the close
 ly related&nbsp\;kernel methods&nbsp\;are well-established and well-studie
 d tools in classical approximation theory. More recently\, they see many u
 ses in other problems in applied and numerical analysis.</p>\n<p>In machin
 e learning\, support vector machines heavily rely on RKHSs. For neural net
 works Barron spaces are connected to certain RKHSs and offer a possibility
  for a theoretical analysis of these networks.</p>\n<p>Another application
  of RKHSs is in high(er)-dimensional approximation. For instance in the fi
 eld of quasi Monte-Carlo methods\, kernel-techniques are used to derive an
  error analysis for high-dimensional quadrature rules. We also developed a
  novel kernel-based approximation method for higher-dimensional meshfree f
 unction reconstruction\, based on Smolyak operators.</p>\n<p>In this talk 
 I will provide an introduction into the theory of RKHSs\, their kernels an
 d associated kernel methods. In particular\, I will focus on a multiscale 
 approximation scheme for rescaled radial basis functions. This method will
  then be used to derive the new&nbsp\;tensor product multilevel method&nbs
 p\;for higher- dimensional meshfree approximation\, which I will discuss i
 n detail.</p>\n\n<p>For further information about the seminar\, please vis
 it this <a href="t3://page?uid=1115" title="Opens internal link in current
  window">webpage</a>.</p>
DTEND;TZID=Europe/Zurich:20230929T120000
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