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CATEGORIES:Applied and Computational Analysis
SUMMARY:Quadrature By Rational Approximation - Nick Trefet
 hen (Oxford and Harvard)
DTSTART;TZID=Europe/London:20250619T150000
DTEND;TZID=Europe/London:20250619T160000
UID:TALK232768AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/232768
DESCRIPTION:Many numerical algorithms rely on quadrature formu
 las such as Gauss quadrature\, the trapezoidal rul
 e\, and their conformal transplantations to specia
 lized domains.  Each quadrature formula can be int
 erpreted as a rational approximation to an analyti
 c function with a branch cut.  Reversing the logic
 \, new quadrature formulas can be quickly derived 
 even for specialized domains by numerical rational
  approximation via the AAA algorithm\, avoiding th
 e need for conformal maps or other analysis.  The 
 poles of the rational approximations delineate bra
 nch cuts\, and the poles and residues are the quad
 rature nodes and weights.  The talk will present t
 en examples: five known problems\, plus a variant 
 for each one. I hope it will change your understan
 ding of quadrature formulas.\n
LOCATION:Centre for Mathematical Sciences\, MR14
CONTACT:Matthew Colbrook
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