Numerical Computation of the Schwarz Function via AAA Rational Approximation
A practical algorithm for computing the Schwarz function S(z) of an analytic arc Gamma - the analytic function with S(z)=conjugate(z) on Gamma that enables analytic continuation across the arc. The method fits S(z) with the AAA algorithm of barycentric rational approximation from sample values on Gamma, giving the first widely usable numerical route to a classically hard-to-compute object and providing the basis for the AAALS solver for Laplace and related planar PDEs. Includes treatment of the multi-valuedness of S(z) away from Gamma.
Springer Nature 2022 LATEX template Numerical computation of the Schwarz function Lloyd N. Trefethen
A numerical-analysis note (Trefethen) giving the first practical method to compute the Schwarz function S(z) of an analytic arc. The Schwarz function is the analytic function satisfying S(z)=conjugat…