A note on piecewise linear and multilinear table interpolation in many dimensions

Authors:
Alan Weiser and Sergio E. Zarantonello

Journal:
Math. Comp. **50** (1988), 189-196

MSC:
Primary 65D05; Secondary 65D15

DOI:
https://doi.org/10.1090/S0025-5718-1988-0917826-0

MathSciNet review:
917826

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Abstract: This note is concerned with *N*-dimensional rectangular table interpolation, where *N* is relatively large (4 to 10). Two interpolants are considered: a piecewise multilinear generalization of piecewise bilinear interpolation on rectangles, and a piecewise linear generalization of piecewise linear interpolation on triangles. We show that the two interpolants have similar approximation properties, but the piecewise linear interpolant is much cheaper to evaluate.

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DOI:
https://doi.org/10.1090/S0025-5718-1988-0917826-0

Article copyright:
© Copyright 1988
American Mathematical Society