Moving least squares interpolation with thin-plate splines and radial basis functions
The author investigates methods based on thin plate splines and on other radial basis functions. It turns out that a small support of the weight function leads to a small support for the spline basis and associated efficiency in the evaluation of the approximant. The moving least squares (MLS) method can then be interpreted as an operator on a function \(f\) generating a certain output. The operator based on polynomials will be denoted \(PMLS\). In general, \(PMLS(f)\) doesn't interpolate \(f\) because \(\dim(P_ m)<n\), where \(P_ m\) is the linear space of bivariate polynomials of degree \(\leq m\). Several examples are given.
scientific article; zbMATH DE number 150174