A linear barycentric rational interpolant on starlike domains

When an approximant is accurate on interval, it only natural to try extend multi-dimensional domains. In the present article we make use of fact that linear rational barycentric interpolants converge rapidly toward analytic and several-times differentiable functions interpolate them two-dimensional starlike domains parametrized in polar coordinates. radial direction, engage at conformally shifted Chebyshev nodes, which exponentially for functions. circular deploy trigonometric interpolants, similarly periodic but now equispaced nodes. We introduce a variant tensor-product interpolant above two schemes prove converges functions–up logarithmic factor–and with order limited by differentiability real (provided boundary enjoys same differentiability). Numerical examples confirm shifts permit one reach much higher accuracy significantly fewer property especially important several dimensions.