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DTSTART:19810329T020000
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UID:news1787@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20250318T095344
DTSTART;TZID=Europe/Zurich:20250328T110000
SUMMARY:Seminar in Numerical Analysis: Daniel Potts (TU Chemnitz)
DESCRIPTION:In this talk\, we present algorithms for the approximation of m
 ultivariate functions. We start with the approximation by trigonometric po
 lynomials based on sampling of multivariate functions on rank-1 lattices o
 r on scattered data. To this end\, we study the approximation of functions
  in periodic Sobolev spaces of dominating mixed smoothness. The proposed a
 lgorithm based mainly on a fast Fourier transforms\, and the arithmetic co
 mplexity of the algorithm depends only on the cardinality of the support o
 f the trigonometric polynomial in the frequency domain. After a detailed i
 ntroduction we will focus on the following questions in more detail.\\r\\n
  	 	We discuss methods where the support of the trigonometric polynomial i
 s unknown. 	 	 	We present a method based on the analysis of variance (ANO
 VA) decomposition that aims to detect the structure of the function\, i.e.
 \, find out which dimension and dimension interactions are important. This
  information is then utilized in obtaining an approximation for the functi
 on. 	 	 	Based on these methods we develop an efficient\, non-intrusive\, 
 adaptive algorithm for the solution of elliptic partial differential equat
 ions. 	 \\r\\n\\r\\nFor further information about the seminar\, please vis
 it this webpage [t3://page?uid=1115].
X-ALT-DESC:<p>In this talk\, we present algorithms for the approximation of
  multivariate functions. We start with the approximation by trigonometric 
 polynomials based on sampling of multivariate functions on rank-1 lattices
  or on scattered data. To this end\, we study the approximation of functio
 ns in periodic Sobolev spaces of dominating mixed smoothness. The proposed
  algorithm based mainly on a fast Fourier transforms\, and the arithmetic 
 complexity of the algorithm depends only on the cardinality of the support
  of the trigonometric polynomial in the frequency domain. After a detailed
  introduction we will focus on the following questions in more detail.</p>
 \n<ul> 	<li> 	<p>We discuss methods where the support of the trigonometric
  polynomial is unknown.</p> 	</li> 	<li> 	<p>We present a method based on 
 the analysis of variance (ANOVA) decomposition that aims to detect the str
 ucture of the function\, i.e.\, find out which dimension and dimension int
 eractions are important. This information is then utilized in obtaining an
  approximation for the function.</p> 	</li> 	<li> 	<p>Based on these metho
 ds we develop an efficient\, non-intrusive\, adaptive algorithm for the so
 lution of elliptic partial differential equations.</p> 	</li> </ul>\n\n<p>
 For further information about the seminar\, please visit this <a href="t3:
 //page?uid=1115" title="Opens internal link in current window">webpage</a>
 .</p>
DTEND;TZID=Europe/Zurich:20250328T123000
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