The pseudo-Chebyshev wavelets and its applications in the error of the functions of bounded variation

Abstract

This paper introduces a novel computational approach aimed at ad-
dressing the challenges of approximation theory. The method is based
upon pseudo-Chebyshev wavelet approximations, a concept rst intro-
duced by Lal et al. in June 2022, which are constructed using pseudo-
Chebyshev functions. The paper details the method, followed by an anal-
ysis of the error for a given function. To showcase the accuracy and
eciency of the pseudo-Chebyshev wavelet approximation method, key
ndings are demonstrated through an example. Additionally, the paper
derives error of a function associated with functions of bounded varia-
tion using the pseudo-Chebyshev wavelet by the orthogonal projection
operators, establishing these estimators as notably sharper and the best
possible in theory of wavelet analysis.