article · Mathematics of Computation · 1972

Generalized recursive multivariate interpolation

Cited by 5Open access

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 <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="n"> <mml:semantics> <mml:mi>n</mml:mi> <mml:annotation encoding="application/x-tex">n</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-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 <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="n"> <mml:semantics> <mml:mi>n</mml:mi> <mml:annotation encoding="application/x-tex">n</mml:annotation> </mml:semantics> </mml:math> </inline-formula> dimensions.

Cite this paper

APA 7

McKinney, E. (1972). Generalized recursive multivariate interpolation. Mathematics of Computation, 26(119), 723–735. https://doi.org/10.1090/s0025-5718-1972-0341797-x

MLA 9

McKinney, Earl. “Generalized recursive multivariate interpolation.” Mathematics of Computation, vol. 26, no. 119, 1972, pp. 723–35, https://doi.org/10.1090/s0025-5718-1972-0341797-x.

Chicago

McKinney, Earl. 1972. “Generalized recursive multivariate interpolation.” Mathematics of Computation 26 (119): 723–35. https://doi.org/10.1090/s0025-5718-1972-0341797-x.

Harvard

McKinney, E. (1972) ‘Generalized recursive multivariate interpolation’, Mathematics of Computation, 26(119), pp. 723–735. Available at: https://doi.org/10.1090/s0025-5718-1972-0341797-x.

BibTeX

@article{mckinney1972generalized,
  title = {{Generalized recursive multivariate interpolation}},
  author = {McKinney, Earl},
  journal = {Mathematics of Computation},
  volume = {26},
  number = {119},
  pages = {723--735},
  year = {1972},
  doi = {10.1090/s0025-5718-1972-0341797-x}
}

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