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

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. (C) 2021 Elsevier Ltd. All rights reserved.