Multivariate approximation by PDE splines

Authors:
M. Pasadas;M. L. Rodríguez
Affiliations:
Dep. de Matemática Aplicada, Universidad de Granada, 18071 Granada, Spain;Dep. de Matemática Aplicada, Universidad de Granada, 18071 Granada, Spain
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

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Abstract

This work deals with an approximation method for multivariate functions from data constituted by a given data point set and a partial differential equation (PDE). The solution of our problem is called a PDE spline. We establish a variational characterization of the PDE spline and a convergence result of it to the function which the data are obtained. We estimate the order of the approximation error and finally, we present an example to illustrate the fitting method.