Polyharmonic splines on grids Z x aZ^n and their limits
Radial Basis Functions (RBF) have found a wide area of applications. We consider the case of polyharmonic RBF (called sometimes polyharmonic splines) where the data are on special grids of the form ℤ × aℤn having practical importance. The main purpose of the paper is to consider the behavior of the...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2005 |
| País: | España |
| Institución: | Universidad de La Rioja (UR) |
| Repositorio: | RIUR. Repositorio Institucional de la Universidad de La Rioja |
| OAI Identifier: | oai:portal.dialnet.es:doc/5bbc68eab750603269e8119a |
| Acceso en línea: | https://investigacion.unirioja.es/documentos/5bbc68eab750603269e8119a |
| Access Level: | acceso abierto |
| Palabra clave: | Interpolation Polyharmonic splines Polysplines Radial basis functions |
| Sumario: | Radial Basis Functions (RBF) have found a wide area of applications. We consider the case of polyharmonic RBF (called sometimes polyharmonic splines) where the data are on special grids of the form ℤ × aℤn having practical importance. The main purpose of the paper is to consider the behavior of the polyharmonic interpolation splines I a on such grids for the limiting process a → 0, a > 0. For a large class of data functions defined on ℝ × ℝn it turns out that there exists a limit function I. This limit function is shown to be a polyspline of order p on strips. By the theory of polysplines we know that the function I is smooth up to order 2 (p - 1) everywhere (in particular, they are smooth on the hyperplanes {j} × ℝn, which includes existence of the normal derivatives up to order 2 (p - 1)) while the RBF interpolants Ia are smooth only up to the order 2p - n - 1. The last fact has important consequences for the data smoothing practice. © 2005 American Mathematical Society. |
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