✍ Scribed by M. Pasadas; M.L. Rodríguez
No coin nor oath required. For personal study only.
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.
📜 SIMILAR VOLUMES
In this paper we give the theoretical analysis for the combination of two ideas in numerical analysis. The first is to approximate the Tchebycheff approximation to a function over a continuum, X, in R M by Tchebycheff approximations over finite, discrete subsets of X, cf. [4, 5, 7, and 8], and the s
Given a convex function \(f\) without any smoothness requirements on its derivatives, we estimate its error of approximation by \(\mathbf{C}^{1}\) convex quadratic splines in terms of \(\omega_{3}(f, 1 / n)\). C 1993 Academic Press, Inc.