Lagrange polynomials of lower sets
نویسندگان
چکیده
A lower set of nodes is a subset of a grid that can be indexed by a lower set of indices. In order to apply the Lagrange interpolation formula, it is convenient to express the Lagrange fundamental polynomials as sums of few terms. We present such a formula for the Lagrange interpolation formula in two variables. In the general multidimensional case, we express the Lagrange fundamental polynomials in d variables in terms of Lagrange fundamental polynomials in d −1 variables. Applications to the problem of computing Lebesgue constants of lower sets are included.
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