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DTSTART:19700329T010000
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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Polynomial approximation of high-dimensional funct
 ions on irregular domains - Ben Adcock (Simon Fras
 er University)
DTSTART;TZID=Europe/London:20180208T090000
DTEND;TZID=Europe/London:20180208T100000
UID:TALK100195AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/100195
DESCRIPTION:<span>Co-author: Daan Huybrechs		(KU Leuven)      
   <br></span><span><br>Smooth\, multivariate funct
 ions defined on tensor domains can be approximated
  using orthonormal bases formed as tensor products
  of one-dimensional orthogonal polynomials.  On th
 e other hand\, constructing orthogonal polynomials
  in irregular domains is difficult and computation
 ally intensive.  Yet irregular domains arise in ma
 ny applications\, including uncertainty quantifica
 tion\, model-order reduction\, optimal control and
  numerical PDEs.  In this talk I will introduce a 
 framework for approximating smooth\, multivariate 
 functions on irregular domains\, known as polynomi
 al frame approximation.  Importantly\, this approa
 ch corresponds to approximation in a frame\, rathe
 r than a basis\; a fact which leads to several key
  differences\, both theoretical and numerical in n
 ature.  However\, this approach requires no orthog
 onalization or parametrization of the domain bound
 ary\, thus making it suitable for very general dom
 ains\, including a priori unknown domains.  I will
  discuss theoretical result s for the approximatio
 n error\, stability and sample complexity of this 
 approach\, and show its suitability for high-dimen
 sional approximation through independence (or weak
  dependence) of the guarantees on the ambient dime
 nsion d.  I will also present several numerical re
 sults\, and highlight some open problems and chall
 enges.</span>
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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