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Bivariate Lagrange interpolation at the Chebyshev nodes

2010
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Proceedings of the American Mathematical Society
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We discuss Lagrange interpolation on two sets of nodes in two dimensions where the coordinates of the nodes are Chebyshev points having either the same or opposite parity. We use a formula of Xu for Lagrange polynomials to obtain a general interpolation theorem for bivariate polynomials at either set of Chebyshev nodes. An extra term must be added to the interpolation formula to handle all polynomials with the same degree as the Lagrange polynomials. We express this term as a specifically

doi:10.1090/s0002-9939-2010-10581-6
fatcat:wu37ikh65fdahefvszjpx5bu2a