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On the Eeciency of Interpolation by Radial Basis Functions
| Content Provider | Semantic Scholar |
|---|---|
| Author | Schaback, Robert |
| Copyright Year | 1997 |
| Abstract | We study the computational complexity, the error behavior, and the numerical stability of interpolation by radial basis functions. It turns out that these issues are intimately connected. For the case of compactly supported radial basis functions, we consider the possibility of getting reasonably good reconstructions of d-variate functions from N data at O(Nd) computational cost and give some supporting theoretical results and numerical examples. scattered locations x j 2 IR d , we want to recover a function f on some given domain IR d that contains X. Under certain assumptions to be stated below, an optimal reconstruction takes the form of interpolation by another function s 2 S C(IR d) with s(x k) = f(x k); 1 k N. Due to the Mairhuber{Curtis 3] theorem, the space S of interpolants must depend on X, as is the case for classical splines and nite elements. However, the space S also depends on the continuity requirements that we shall additionally impose, and these have to match those of f. We x them by picking a (large) function space F that contains f and consists of real-valued functions on. Under the assumptions F is a real Hilbert space, the point evaluation functionals x for x 2 are continuous on F (i.e., elements of the dual space F), the x are linearly independent if they are distinct, the space S is optimally chosen for the above recovery problem if it takes the form ISBN 1-xxxxx-xxx-x. All rights of reproduction in any form reserved. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://num.math.uni-goettingen.de/schaback/research/papers/OtEoIbRBF.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
