Multiscale support vector regression method in Sobolev spaces on bounded domains. (English) Zbl 1316.65024
Using the very efficient approach of approximating functions from spaces spanned by radial basis functions (especially for meshless approximations, that is from scattered data), the authors study support vector regression in order to approximate functions. These are taken from general classes of Sobolev spaces and allowed to be defined over bounded domains. Convergence results are offered employing radial basis functions of various sorts. A special emphasis is given to multiscale support vector regression, used also for approximating rough and noisy data in a number of numerical examples.
Reviewer: Martin D. Buhmann (Gießen)
MSC:
| 65D15 | Algorithms for approximation of functions |
| 65J10 | Numerical solutions to equations with linear operators |
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
Keywords:
multiscale analysis; radial basis functions; support vector regression; convergence; Sobolov space; numerical exampleReferences:
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