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Multiquadric Pre-Wavelets on Non-Equally Spaced Centres
(1994)SAM Research ReportIn this paper, we identify univariate prewavelets on spaces spanned by translates of multiquadric functions and other radial basis functions with emnon-equally spaced/em centres (or "knots"). Although the multiquadric function and its relations are our prime examples, the theory is sufficiently broad to admit prewavelets from other radial basis function spaces as well.Report -
Knot removal with radial function interpolation
(1994)SAM Research ReportIn this note we study interpolants to $n$-variate, real valued functions from radial function spaces, \ie spaces that are spanned by radially symmetric functions $\varphi(\|\cdot - x_{j} \|_2)$ defined on $\R^n$. Here $\| \cdot \|_2$ denotes the Euclidean norm, $\varphi : \R_+ \to \R$ is a given "radial (basis) function" which we take here to be $\varphi (r) = ( r^2 + c^2)^{\beta /2}$, $-n \leq \beta < 0$, and the $\{x_j \} \subset \R^n$ ...Report -
Pre-Wavelets on Scattered Knots and from Radial Function Spaces: A Review
(1994)SAM Research ReportWe review recent work on univariate prewavelets that are either spline prewavelets on non-equally spaced knots or prewavelets from spaces spanned by translates of radial basis functions with non-equally spaced centres. Some of the results on radial basis functions we present apply to more than one dimension as well, so long as the centres are again confined to a grid.Report