Multivariate polysplines : applications to numerical and wavelet analysis Multivariate polysplines are a new mathematical technique that has arisen from a synthesis of approximation theory and the theory of partial differential equations. It is an invaluable means to interpolate practical data with smooth functions. Multivariate polysplines have applications in the design of surfaces and smoothing that are essential in computer aided geometric design (CAGD and CAD CAM systems) geophysics magnetism geodesy geography wavelet analysis and signal and image processing. In many cases involving practical data in these areas polysplines are proving more effective than well established methods such as kKriging radial basis functions thin plate splines and minimum curvature. Part 1 assumes no special knowledge of partial differential equations and is intended as a graduate level introduction to the topic Part 2 develops the theory of cardinal Polysplines which is a natural generalization of Schoenbergs beautiful one dimensional theory of cardinal splines. Part 3 constructs a wavelet analysis using cardinal Polysplines. The results parallel those found by Chui for the one dimensional case. Part 4 considers the ultimate generalization of Polysplines on manifolds for a wide class of higher order elliptic operators and satisfying a Holladay variational property Front Cover; Multivariate Polysplines: Applications to Numerical and Wavelet Analysis; Copyright Page; Contents; Preface; Chapter 1. Introduction; 1.1 Organization of material; 1.2 Audience; 1.3 Statements; 1.4 Acknowledgements; 1.5 The polyharmonic paradigm; Part I: Introduction to polysplines; Chapter 2. One dimensional linear and cubic splines; Chapter 3. The two dimensional case: data and smoothness concepts; Chapter 4. The objects concept: harmonic and polyharmonic functions in rectangular domains in R2; Chapter 5. Polysplines on strips in R2