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SUMMARY:PathFinder: a toolbox for oscillatory integrals by deforming into 
 the complex plane - Daan Huybrechs (KU Leuven)
DTSTART:20191209T113000Z
DTEND:20191209T123000Z
UID:TALK135436@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:We present PathFinder\, a Matlab toolbox developed by Andrew G
 ibbs for the computation of oscillatory integrals. The methods are based o
 n the numerical evaluation of line integrals in the complex plane\, which 
 mostly follow paths of steepest descent. The toolbox aims for automation a
 nd robustness: the path deformation is found fully automatically\, but the
  paths correspond to those of steepest descent only if doing so has guaran
 tees of correctness. We face a trade-off between achieving asymptotic orde
 rs of accuracy\, i.e. increasing accuracy with increasing frequency much l
 ike asymptotic expansions\, and reliable accuracy. In the toolbox we aim f
 or the former\, but give precedence to the latter. We conclude with an exa
 mple of scattering integrals with phase functions that may have clusters o
 f coalescing saddle points.
LOCATION:Seminar Room 1\, Newton Institute
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