Knot removal with radial function interpolation
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1994-09
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Abstract
In 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 $\{x_j \} \subset \R^n$ are prescribed "centres", or knots. We analyse the effect of removing a knot from a given interpolant, in order that in applications one can see how many knots can be eliminated from an interpolant so that the interpolant remains within a given tolerance from the original one.
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1994-09
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Seminar for Applied Mathematics, ETH Zurich
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02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics