Wavelet packets: uniform approximation and numerical integration. (English) Zbl 1440.42173
Summary: In this paper, it is proved that under some conditions, wavelet packet basis of \(L^2(\mathbb{R})\) can be used as a tool for the uniform approximation of an \(M\)-times \((M>0)\) continuously differentiable and square integrable function \(f\). Sufficient conditions which establish that the approximations of wavelet packet sequences of square integrable function \(f\) at lower levels are uniformly reliable and they uniformly approach zero as \(j\to\infty\) are given. Finally, a method based on wavelet packet expansion to find the definite integral of a function in \(L^2(\mathbb{R})\) is given and its error analysis has been discussed.
MSC:
| 42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |
| 42A38 | Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type |
| 65T60 | Numerical methods for wavelets |
| 41A35 | Approximation by operators (in particular, by integral operators) |
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