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

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.