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SUMMARY:Through the Kaleidoscope\; Symmetries\, Groups and Chebyshev Appro
 ximations from a Computational Point of View - Hans Z. Munthe-Kaas (Univer
 sity of Bergen)
DTSTART:20120510T140000Z
DTEND:20120510T150000Z
UID:TALK36662@talks.cam.ac.uk
CONTACT:Carola-Bibiane Schoenlieb
DESCRIPTION:Classical univariate Chebyshev polynomials are fundamental obj
 ects in computational mathematics. Their ubiquity in applications is summa
 rized by the quote: "Chebyshev polynomials are everywhere dense in numeric
 al analysis" (perhaps due to George Forsythe). Most of the useful properti
 es of Chebyshev polynomials arise from their tight connections to group th
 eory. From this perspective\, multivariate Chebyshev polynomials appear as
  natural generalizations\, constructed by a kaleidoscope of mirrors acting
  upon R^n (i.e. affine Weyl groups). Multivariate Chebyshev polynomials we
 re first introduced by Koornwinder already in 1974\, but they have only ve
 ry recently been applied in computational mathematics. The fact that the m
 ultivariate polynomials are orthogonal on domains related to triangles\, t
 etrahedra and higher dimensional simplexes\, rises the important question 
 of their applicability in triangle-based spectral element methods for PDEs
 . We have developed general software tools with such applications in mind.
LOCATION:MR14\, CMS
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