On the Continuity of Multivariate Lagrange Interpolation at Chung-Yao Lattices
arXiv:1112.286916 citationsh-index: 15
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Provides a theoretical guarantee for convergence of a specific interpolation scheme, relevant to approximation theory researchers.
The paper identifies a geometric condition ensuring that multivariate Lagrange interpolation at Chung-Yao lattices converges to the Taylor polynomial for sufficiently differentiable functions.
We give a natural geometric condition that ensures that sequences of Chung-Yao interpolation polynomials (of fixed degree) of sufficiently differentiable functions converge to a Taylor polynomial.