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.

约束模拟切比雪夫最小二乘插值是一种单变量多项式插值技术，用于减少龙格现象。它利用了模拟 Chebyshev 节点上插值的最优性，即由模仿 Chebyshev-Lobatto 节点行为的节点形成的统一网格的子集。网格的其他节点不会被丢弃，而是用于同时回归以提高模拟切比雪夫子集插值的近似精度。在本文中，我们以两种不同的方式将单变量约束模拟切比雪夫最小二乘插值扩展到双变量情况，依赖于张量积插值和模拟帕多瓦节点的插值。数值实验证明了这种扩展的有效性。