Quasi-Positive Delta Sequences and Their Applications in Wavelet Approximation

A sufficient literature is available for the wavelet error of approximation of certain functions in the L2-norm. There is no work in context of multiresolution approximation of a function in the sense of sup-error. In this paper, for the first time, wavelet estimator for the approximation of a function f belonging to Lipα[a,b] class under supremum norm has been obtained. Working in this direction, four new theorems on the wavelet approximation of a function f belonging to Lipα,0<α≤1 class using the projection Pmf of its wavelet expansions have been estimated. The calculated estimator is best possible in wavelet analysis

Quasi-Positive Delta Sequences and Their Applications in Wavelet Approximation

A sufficient literature is available for the wavelet error of approximation of certain functions in the 2 -norm. There is no work in context of multiresolution approximation of a function in the sense of sup-error. In this paper, for the first time, wavelet estimator for the approximation of a function belonging to Lip [ , ] class under supremum norm has been obtained. Working in this direction, four new theorems on the wavelet approximation of a function belonging to Lip , 0 &lt; ≤ 1 class using the projection of its wavelet expansions have been estimated. The calculated estimator is best possible in wavelet analysis

Error bounds of a function related to generalized Lipschitz class via the pseudo-Chebyshev wavelet and its applications in the approximation of functions

In this paper, a new computation method derived to solve the problems of approximation theory. This method is based upon pseudo-Chebyshev wavelet approximations. The pseudo-Chebyshev wavelet is being presented for the first time. The pseudo-Chebyshev wavelet is constructed by the pseudo-Chebyshev functions. The method is described and after that the error bounds of a function is analyzed. We have illustrated an example to demonstrate the accuracy and efficiency of the pseudo-Chebyshev wavelet approximation method and the main results. Four new error bounds of the function related to generalized Lipschitz class via the pseudo-Chebyshev wavelet are obtained. These estimators are the new fastest and best possible in theory of wavelet analysis