Cardinal interpolation with differences of tempered functions Academic Article uri icon

abstract

  • In this paper, we investigate the existence and uniqueness of cardinal interpolants associated with functions arising from the kth order iterated discrete Laplacian {down triangle, open}k applied to certain radial basis functions. In particular, we concentrate on determining, for a given radial function Φ, which functions {down triangle, open}kΦ give rise to cardinal interpolation operators which are both bounded and invertible ℓ2 (Z3). In addition to solving the cardinal interpolation problem (CIP) associated with such functions {down triangle, open}kΦ, our approach provides a unified framework and simpler proofs for the CIP associated with polyharmonic splines and Hardy multiquadrics. © 1992.

author list (cited authors)

  • Chui, C. K., Ward, J. D., & Jetter, K.

citation count

  • 10

publication date

  • December 1992