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Lagrange polynomials of a complex variable for two‐dimensional interpolation
Author(s) -
Bates R. H. T.,
Milner M. O.
Publication year - 1977
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620111204
Subject(s) - lagrange polynomial , interpolation (computer graphics) , variable (mathematics) , grid , mathematics , trigonometric interpolation , dimension (graph theory) , trilinear interpolation , nearest neighbor interpolation , inverse quadratic interpolation , polynomial interpolation , multivariate interpolation , algorithm , linear interpolation , algebra over a field , bilinear interpolation , mathematical analysis , computer science , geometry , pure mathematics , polynomial , artificial intelligence , motion (physics) , statistics
We recognize that established techniques permit two‐dimensional interpolation to be accomplished efficiently as well as accurately when the grid of points, on which the data is available, is regular. Existing methods suitable for irregular grids are computationally protracted. We show that by using Lagrange polynomials of a complex variable we can interpolate, almost as conveniently as in one dimension, from an irregular grid onto particular points lying on parallel lines. Standard one‐dimensional interpolation schemes can then be used to complete the two‐dimensional interpolation. We discuss how, in any particular instance, the order of the Lagrange polynomials is chosen, and we present the results of a computational test of our method.