Abstract

In this paper, linear wavelet approximation of a functions $f$ belonging to Lip$\xi,$ and $Lip(\xi,p), 1 \leq p < \infty,$ have been determined by using Haar scaling function and Haar wavelet series. A non-linear wavelet approximation of function belonging $L^2(\mathbb{R})$ and Lip$\alpha$ class has been obtained. The comparison of the order of linear and non-linear approximations have been studied. It is observed that a non-linear approximation error is better and sharper than linear approximation error.

Keywords and Phrases

Lip$\alpha$ class of functions, Lip$(\alpha, p)$ class of functions, Lip$\xi$ class of functions, Lip$(\xi,p)$ class of functions, Multiresolution analysis, Scaling function $\phi$, Linear approximation, Non-linear approximation.

A.M.S. subject classification

40A30, 42C15, 42A16, 42C40, 65T60, 65L10, 65L60, 65R20.

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