Several enhancements to hermite-based approximation of one-variable functions

Abstract

Several enhancements and comments to Hermite-based one-variable function approximation are presented. First of all we prove that a constant bias extracted from the function contributes to the error decrease. We demonstrate how to choose that bias. Secondly we show how to select a basis among orthonormal functions to achieve minimum error for a fixed dimension of an approximation space. Thirdly we prove that loss of orthonormality due to truncation of the argument range of the basis functions does not effect the overall error of approximation and the expansion coefficients. We show how this feature can be used. An application of the obtained results to ECG data compression is presented. © Springer-Verlag Berlin Heidelberg 2008.