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I the interpolation theory of radial basis functions (1992).
| Content Provider | CiteSeerX |
|---|---|
| Author | Baxter, Charles Baxter, B. J. C. John, Bradley |
| Abstract | The problem of interpolating functions of d real variables (d> 1) occurs naturally in many areas of applied mathematics and the sciences. Radial basis function methods can provide interpolants to function values given at irregularly positioned points for any value of d. Further, these interpolants are often excellent approxi-mations to the underlying function, even when the number of interpolation points is small. In this dissertation we begin with the existence theory of radial basis function interpolants. It is first shown that, when the radial basis function is a p-norm and 1 < p < 2, interpolation is always possible when the points are all different and there are at least two of them. Our approach extends the analysis of the case p = 2 devised in the 1930s by Schoenberg. We then show that interpolation is not always possible when p> 2. Specifically, for every p> 2, we construct a set of different points in some R d for which the interpolation matrix is singular. This construction seems to have no precursor in the literature. The greater part of this work investigates the sensitivity of radial basis func- |
| File Format | |
| Publisher Date | 1992-01-01 |
| Access Restriction | Open |
| Subject Keyword | Real Variable Interpolation Theory Radial Basis Function Radial Basis Function Method Interpolation Point Excellent Approxi-mations Interpolation Matrix Radial Basis Function Existence Theory Underlying Function Radial Basis Func Radial Basis Function Interpolants Applied Mathematics Different Point Many Area |
| Content Type | Text |
| Resource Type | Thesis |
