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Mathematics of Computation

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Generalized recursive multivariate interpolation

Author: Earl H. McKinney
Journal: Math. Comp. 26 (1972), 723-735
MSC: Primary 65D05; Secondary 41A63
MathSciNet review: 0341797
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Abstract: A generalized recursive interpolation technique for a set of linear functionals over a set of general univariate basis functions has been previously developed. This paper extends these results to restricted multivariate interpolation over a set of general multivariate basis functions. When the data array is a suitable configuration (e.g., an $ n$-dimensional simplex), minimal degree multivariate interpolating polynomials are produced by this recursive interpolation scheme. By using product rules, recursive univariate interpolation applied to each variable singly produces multivariate interpolating polynomials (not of minimal degree) when the data are arranged in a hyper-rectangular array. By proper ordering of points in a data array, multivariate polynomial interpolation is accomplished over other arrays such as diamonds and truncated diamonds in two dimensions and their counterparts in $ n$ dimensions.

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Keywords: Recursive multivariate interpolation, repeated recursive univariate interpolation, hyper-rectangular array, basis functions
Article copyright: © Copyright 1972 American Mathematical Society

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