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SUMMARY:Quadrature By Rational Approximation - Nick Trefethen (Oxford and 
 Harvard)
DTSTART:20250619T140000Z
DTEND:20250619T150000Z
UID:TALK232768@talks.cam.ac.uk
CONTACT:Matthew Colbrook
DESCRIPTION:Many numerical algorithms rely on quadrature formulas such as 
 Gauss quadrature\, the trapezoidal rule\, and their conformal transplantat
 ions to specialized domains.  Each quadrature formula can be interpreted a
 s a rational approximation to an analytic function with a branch cut.  Rev
 ersing the logic\, new quadrature formulas can be quickly derived even for
  specialized domains by numerical rational approximation via the AAA algor
 ithm\, avoiding the need for conformal maps or other analysis.  The poles 
 of the rational approximations delineate branch cuts\, and the poles and r
 esidues are the quadrature nodes and weights.  The talk will present ten e
 xamples: five known problems\, plus a variant for each one. I hope it will
  change your understanding of quadrature formulas.\n
LOCATION:Centre for Mathematical Sciences\, MR14
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