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SUMMARY:Polynomial approximation of high-dimensional functions on irregula
 r domains - Ben Adcock (Simon Fraser University)
DTSTART:20180208T090000Z
DTEND:20180208T100000Z
UID:TALK100195@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:<span>Co-author: Daan Huybrechs		(KU Leuven)        <br></span
 ><span><br>Smooth\, multivariate functions defined on tensor domains can b
 e approximated using orthonormal bases formed as tensor products of one-di
 mensional orthogonal polynomials.  On the other hand\, constructing orthog
 onal polynomials in irregular domains is difficult and computationally int
 ensive.  Yet irregular domains arise in many applications\, including unce
 rtainty quantification\, model-order reduction\, optimal control and numer
 ical PDEs.  In this talk I will introduce a framework for approximating sm
 ooth\, multivariate functions on irregular domains\, known as polynomial f
 rame approximation.  Importantly\, this approach corresponds to approximat
 ion in a frame\, rather than a basis\; a fact which leads to several key d
 ifferences\, both theoretical and numerical in nature.  However\, this app
 roach requires no orthogonalization or parametrization of the domain bound
 ary\, thus making it suitable for very general domains\, including a prior
 i unknown domains.  I will discuss theoretical result s for the approximat
 ion error\, stability and sample complexity of this approach\, and show it
 s suitability for high-dimensional approximation through independence (or 
 weak dependence) of the guarantees on the ambient dimension d.  I will als
 o present several numerical results\, and highlight some open problems and
  challenges.</span>
LOCATION:Seminar Room 1\, Newton Institute
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