APPROXIMATION BY HAAR WAVELET AND THEIR ORDER OF APPROXIMATION IN DIFFERENT SPACES

Authors

  • M.R. Islam Mathematics Discipline, Khulna University, Khulna 9208, Bangladesh
  • M.A. Huda Mathematics Discipline, Khulna University, Khulna 9208, Bangladesh
  • S.F Ahmmed Mathematics Discipline, Khulna University, Khulna 9208, Bangladesh
  • S.M.A. Rahman Mathematics Discipline, Khulna University, Khulna 9208, Bangladesh

DOI:

https://doi.org/10.53808/KUS.2007.8.1.0628-PS

Keywords:

Approximation, wavelet approximation, HAAR wavelet, approximation order, space

Abstract

Wavelet analysis uses as a new class of orthogonal expansion in  with regularity-approximation properties. In this study, we approximate any general function in  by Haar wavelet in different smoothness spaces such as Lebesgue space, Lipschitz continuous space, Sobolev and Besov spaces.

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References

Christensen, O. and Christensen, K.L. 2004. Approximation Theory, From Taylor Polynomials to Wavelets. Brikhäuser, Boston.

Cohen, A. 2003. Numerical Analysis of Wavelet Methods. Elsevier, U.S.A.

Cohen, A.; Daubechies, I. and Feauveau, J. 1992. Biorthogonal basis of compactly supported wavelets. Journal of Pure and Applied Mathematics, 45: 485-560.

deVore, R.A. 1998. Non-linear approximation. Acta Numerica, Cambridge University Press, pp. 51-150.

Islam, M.R. 2005. Approximation by Wavelets. M.S. Thesis, KFUPM, Saudi Arabia.

Meyer, Y. 1993. Wavelets: their past and their future. In: Meyer, Y. and Roques, S. (eds.), Progress in Wavelet Analysis and its Applications. Editions Frontiers, Gif-sur-Yvette, pp. 9-18.

Natanson, I.P. 1949. Constructive Function Theory. Mosco.

Walnut, D.F. 2001. An Introduction to Wavelet Analysis. Brikhäuser, Boston.

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Published

26-05-2007

How to Cite

[1]
M. Islam, M. Huda, S. . . Ahmmed, and S. Rahman, “APPROXIMATION BY HAAR WAVELET AND THEIR ORDER OF APPROXIMATION IN DIFFERENT SPACES”, Khulna Univ. Stud., pp. 161–167, May 2007.

Issue

Section

Physical Science

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