Multivariate scattered data fitting

Scattered Data Fitting on the Sphere

We discuss several approaches to the problem of interpolating or approximating data given at scattered points lying on the surface of the sphere. These include methods based on spherical harmonics, tensor-product spaces on a rectangular map of the sphere, functions deened over spherical triangulations, spherical splines, spherical radial basis functions, and some associated multi-resolution met...

The multivariate spline method for numerical solution of partial differential equations and scattered data fitting

The Multivariate Spline Method for Scattered Data Fitting and Numerical Solutions of Partial Differential Equations

Multivariate spline functions are smooth piecewise polynomial functions over triangulations consisting of n-simplices in the Euclidean space IR. A straightforward method for using these spline functions to fit given scattered data and numerically solve elliptic partial differential equations is presented . This method does not require constructing macro-elements or locally supported basis funct...

Reconstruction of Multivariate Functions from Scattered Data

Monotonicity Preserving Approximation of Multivariate Scattered Data ∗

This paper describes a new method of monotone interpolation and smoothing of multivariate scattered data. It is based on the assumption that the function to be approximated is Lipschitz continuous. The method provides the optimal approximation in the worst case scenario and tight error bounds. Smoothing of noisy data subject to monotonicity constraints is converted into a quadratic programming ...