Generalizations of the constrained mock-Chebyshev least squares in two variables: Tensor product vs total degree polynomial interpolation

Abstract

The constrained mock-Chebyshev least squares interpolation is a univariate polynomial interpolation technique exploited to cut-down the Runge phenomenon. It takes advantage of the optimality of the interpolation on the mock-Chebyshev nodes, i.e. the subset of the uniform grid formed by nodes that mimic the behavior of Chebyshev–Lobatto nodes. The other nodes of the grid are not discarded, rather they are used in a simultaneous regression to improve the accuracy of the approximation of the mock-Chebyshev subset interpolant. In this paper we extend the univariate constrained mock-Chebyshev least squares interpolation to the bivariate case in two different ways, relying on the tensor product interpolation and on the interpolation at the mock-Padua nodes. Numerical experiments demonstrate the effectiveness of such extensions.