Scattered Data Interpolation: Radial Basis and Other Methods

This chapter presents some techniques for solving scattered data interpolation for functional data. It describes the way interpolants are computed and evaluated using radial basis functions and some other local methods. The overall idea for the evaluation of the interpolant is to break down the evaluation into two parts: contributions from the near terms and contributions from the far term. To define what is near and what is far, the data is structured hierarchically. The chapter briefly describes some existence and uniqueness properties of the interpolants. Scattered data interpolation and approximation problems arise in a variety of applications including meteorology, hydrology, oceanography, computer graphics, computer-aided geometric design, and scientific visualization. There exist several variants of the basic problem. The basic problem, referred to as the functional scattered data problem, is to find a surface that interpolates or approximates a finite set of points. Solutions to the scattered data interpolation or approximation problem are equally varied.

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