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SUMMARY:On the numerical solution of Riemann--Hilbert problems with theta-
 function asymptotics - Thomas Trogdon (University of Washington)
DTSTART:20230725T103000Z
DTEND:20230725T113000Z
UID:TALK202777@talks.cam.ac.uk
DESCRIPTION:We consider the numerical solution of Riemann--Hilbert problem
 s that are asymptotically posed on a union of disjoint intervals. &nbsp\; 
 The singularities present in the solution of the problem are captured accu
 rately using singular weight functions. A collocation method using orthogo
 nal polynomials with respect to these weights is developed. The primary ap
 plications we discuss are to (1) the numerical solution of the computation
  of the finite-genus solutions of the KdV equation and to (2) the computat
 ion of the three-term recurrence coefficients for polynomials orthogonal o
 n multiple intervals. &nbsp\;With regard to (1)\, we give a new numerical 
 method to solve the periodic initial-value problem for the KdV equation an
 d compute large-genus solutions. &nbsp\;For (2)\, an outcome of the work i
 s a new implementation of inner-product free iterative solvers for indefin
 ite linear systems.
LOCATION:Seminar Room 1\, Newton Institute
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