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Legendre Wavelet Expansion of a Function f(x, y) and its Approximation

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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Year of Publication: 2017
Authors:
Shyam Lal, Anavaruddin Ansari
10.5120/ijca2017914819

Shyam Lal and Anavaruddin Ansari. Legendre Wavelet Expansion of a Function f(x, y) and its Approximation. International Journal of Computer Applications 171(6):1-7, August 2017. BibTeX

@article{10.5120/ijca2017914819,
	author = {Shyam Lal and Anavaruddin Ansari},
	title = {Legendre Wavelet Expansion of a Function f(x, y) and its Approximation},
	journal = {International Journal of Computer Applications},
	issue_date = {August 2017},
	volume = {171},
	number = {6},
	month = {Aug},
	year = {2017},
	issn = {0975-8887},
	pages = {1-7},
	numpages = {7},
	url = {http://www.ijcaonline.org/archives/volume171/number6/28182-2017914819},
	doi = {10.5120/ijca2017914819},
	publisher = {Foundation of Computer Science (FCS), NY, USA},
	address = {New York, USA}
}

Abstract

In this paper, two new Legendre Wavelet estimators of a function f of two variable x and y by (2k-1,M; 2k′-1,M′)th partials sums of their Legendre wavelet series are obtained. These estimators are sharper and better in Wavelet Analysis.

References

  1. A. Zygmund, Trigonometric Series Vol. I, Cambridge University Press, 1959.
  2. M. Razzaghi and S. Yousefi(2001), “ The Legendre Wavelet operational Matrix of Integration”, “ Intenational Journal of Systems Sciences ” Vol. 32, No. 4, pp. 495-502.
  3. M. R. Islam, S. F. Ahemmed and S. M. A Rahman(2006), “Comparison of Wavelet Approximation Order in different smoothness spaces” “International Journal of Mathematics and Mathematical Sciences”, Volume 2006, Article ID 63670, 1-7, DOI 10. 1155/IJMMS/2006/63670.
  4. Nanshan Liu, En- Bing Lin(2009), “ LegendreWavelet Method for Numerical Solutions of Partial Differential Equations”, “ Willey Inter Science”, DOI 10.1002/num.20417.
  5. Shyam Lal and Manoj Kumar(2013), “ Approximation of functions of space of L2(R) by wavelet expansions”, “ Lobacheveskii Journal of Mathematics”, Vol. 34, No.2, pp. 163- 172,
  6. Shyam Lal and Susheel Kumar, “ Best Wavelet Approximation of Functions Belonging to Generalized Lipschitz Class using Haar Scaling function ”, “Thai Journal of Mathematics”(Article in press).

Keywords

Legendre wavelets, wavelet expansion, wavelet approximation, mother wavelet