Approximation of the minmax interpolator

Abstract

We consider approximation of the optimal Yen algorithm (1956) for interpolation from a nonuniformly-spaced grid. Although the Yen interpolator is optimal in many senses, it suffers from severe numerical ill conditioning. We suggest a tradeoff between accuracy in computing the interpolator and accuracy in performing the interpolation. A new interpolator is proposed using Choi's expression (1998) for interpolation error. A strategy is suggested to control the error tradeoff. We also generalize the new interpolator to multiple dimensions. The newly designed sinc-kernel interpolator is compared with the Yen, Choi, and usual sinc interpolator with Jacobian weighting using simulations in both one and two dimensions. We show that the new interpolator is robust. It performs similarly to the Yen algorithm when noise is small and similarly to the Choi algorithm when noise is large.