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

Weiser, Alan; Zarantonello, Sergio E.

doi:10.1090/S0025-5718-1988-0917826-0

A note on piecewise linear and multilinear table interpolation in many dimensions
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by Alan Weiser and Sergio E. Zarantonello PDF

Math. Comp. 50 (1988), 189-196 Request permission

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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