A Numerical Study of the Xu Polynomial Interpolation Formula in Two Variables

摘要

In his paper "Lagrange interpolation on Chebyshev points of two variables" (J. Approx. Theor. 87, 220-238, 1996), Y. Xu proposed a set of Chebyshev like points for polynomial interpolation in the square, and derived a compact form of the corresponding Lagrange interpolation formula. We investigate computational aspects of the Xu polynomial interpolation formula like numerical stability and efficiency, the behavior of the Lebesgue constant, and its application to the reconstruction of various test functions.