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Tricubic Polynomial Interpolation

Garrett Birkhoff
Proceedings of the National Academy of Sciences of the United States of America
Vol. 68, No. 6 (Jun., 1971), pp. 1162-1164
Stable URL: http://www.jstor.org/stable/60295
Page Count: 3
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Tricubic Polynomial Interpolation
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Abstract

A new triangular ``finite element'' is described; it involves the 12-parameter family of all quartic polynomial functions that are ``tricubic'' in that their variation is cubic along any parallel to any side of the triangle. An interpolation scheme is described that approximates quite accurately any smooth function on any triangulated domain by a continuously differentiable function, tricubic on each triangular element.

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