ABSTRACT
Radial basis function methods are tools for multivariable approximation where functions / : lRn —► 1R are approximated from spaces spanned by translates of normally just one function φ : lRn —► IR. The points by which φ is translated are usually called “centres” . The function φ may or may not be a radially symmetric function, i.e., φ = <£>(|| · H2), but for the most common and best studied examples it is, such as the ubiquitous multiquadric function, where φ = y/(·)2 + c2, c being a parameter, or the equally well-known thin plate spline, where φ = (·)2 log(·). This is why these methods are still called radial basis function methods, although their performance depends much more on <£>’s smoothness and growth properties than on its spherical symmetry.
