A new approach for constructing mock-Chebyshev grids

Polynomial interpolation with equidistant nodes is notoriously unreliable due to the Runge phenomenon and is also numerically ill-conditioned. By taking advantage of the optimality of the interpolation processes on Chebyshev nodes, one of the best strategies to defeat the Runge phenomenon is to use the mock-Chebyshev points, which are selected from a satisfactory uniform grid, for polynomial interpolation. Yet little literature exists on the computation of these points. In this study, we investigate the properties of the mock-Chebyshev nodes and propose a subsetting method for constructing mock-Chebyshev grids. Moreover, we provide a precise formula for the cardinality of a satisfactory uniform grid. Some numerical experiments using the points obtained by the method are given to show the effectiveness of the proposed method, and numerical results are also provided.

Automated summary

By studying the properties of mock-Chebyshev nodes and proposing a subsetting method for constructing mock-Chebyshev grids, this study addresses the issue of the Runge phenomenon in polynomial interpolation, providing an exact formula for the cardinality of a satisfactory uniform grid. Numerical experiments using points obtained by the proposed method show its effectiveness, with numerical results also being presented.