Adaptive bivariate Chebyshev approximation

We propose an adaptive algorithm which extends Chebyshev series approximation to bivariate functions, on domains which are smooth transformations of a square. The method is tested on functions with different degrees of regularity and on domains with various geometries. We show also an application to the fast evaluation of linear and nonlinear bivariate integral transforms. Work supported by the research project CPDA028291 “Efficient approximation methods for nonlocal discrete transforms” of the University of Padova, and by the GNCS-INdAM.