Tensor spline approximation

Abstract

The cyclic-shift tensor-factorization interpolation method recently described by de Boor can be used in particular for least-squares fitting of multivariate data on a rectangular grid and for evaluation of the resulting tensor-product splines, taking advantage of existing linear algebra and univariate spline software. We discuss the computational details of this method, pointing out variants and suggesting techniques for dealing with ill-conditioned least-squares problems.