CFP last date
20 May 2024
Call for Paper
June Edition
IJCA solicits high quality original research papers for the upcoming June edition of the journal. The last date of research paper submission is 20 May 2024

Submit your paper
Know more
The week's pick
Responsive image
Enhancing Privacy Preservation: Multi-Attribute Protection with P-Sensitive K-Anonymity

Twinkle Patel Kiran Amin
Random Articles
Reseach Article

Wavelet Approximations using (Λ⋅C1) Matrix-Cesaro Summability Method of Jacobi Series

by Shyam Lal, Manoj Kumar
journal cover thumbnail

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 147 - Number 14
Year of Publication: 2016
Authors: Shyam Lal, Manoj Kumar
10.5120/ijca2016911210

Shyam Lal, Manoj Kumar . Wavelet Approximations using (Λ⋅C1) Matrix-Cesaro Summability Method of Jacobi Series. International Journal of Computer Applications. 147, 14 ( Aug 2016), 1-8. DOI=10.5120/ijca2016911210

@article{ 10.5120/ijca2016911210,
author = { Shyam Lal, Manoj Kumar },
title = { Wavelet Approximations using (Λ⋅C1) Matrix-Cesaro Summability Method of Jacobi Series },
journal = { International Journal of Computer Applications },
issue_date = { Aug 2016 },
volume = { 147 },
number = { 14 },
month = { Aug },
year = { 2016 },
issn = { 0975-8887 },
pages = { 1-8 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume147/number14/25822-2016911210/ },
doi = { 10.5120/ijca2016911210 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T23:52:03.846084+05:30
%A Shyam Lal
%A Manoj Kumar
%T Wavelet Approximations using (Λ⋅C1) Matrix-Cesaro Summability Method of Jacobi Series
%J International Journal of Computer Applications
%@ 0975-8887
%V 147
%N 14
%P 1-8
%D 2016
%I Foundation of Computer Science (FCS), NY, USA
Abstract

In this paper, an application to the approximation by wavelets has been obtained by using matrix-Cesaro (Λ⋅C1) method of Jacobi polynomials. The rapid rate of convergence of matrix-Cesaro method of Jacobi polynomials are estimated. The result of Theorem (6.1) of this research paper is applicable for avoiding the Gibbs phenomenon in intermediate levels of wavelet approximations. There are major roles of wavelet approximations (obtained in this paper) in computer applications. The matrix-Cesaro (Λ⋅C1) method includes (N, pn)⋅C1 method as a particular case. The comparison between the numerical results obtained by the (N, pn)⋅C1 and matrix-Cesaro (Λ⋅C1) summability method reveals a slight improvement concerning the reduction of the excessive oscillations by using the approach of present paper.

References
  1. Osilenker, B. (1999), “Fourier Series in Orthogonal Polynomials”, World Scientific, Singapore.
  2. Szego, G. (1975), “Orthogonal Polynomials”, Amer. Math. Soc. Colloq. Publ., Vol. 23, Amer. Math. Soc., Providence, RI.
  3. Zygmund, A. (1959), “Trigonometric Series”, Vols. I & II, Cambridge University Press, London.
  4. Moricz, F. (2013), “Statistical Convergence of Sequences and Series of Complex Numbers with Applications in Fourier Analysis and Summability”, Analysis Mathematica, Vol. 39, pp. 271-285.
  5. Moricz, F. (2004), “Ordinary convergence follows from statistical summability (C, 1) in the case of slowly decreasing or oscillating sequences”, Colloq. Math., Vol. 99, pp. 207219.
  6. Lal, Shyam and Sharma, Vivek Kumar (2016), “On the Approximation of a Continuous Function f(x; y) by its Two Dimensional Legendre Wavelet Expansion”, International Journal of Computer Applications, Vol. 143 - No. 6, pp. 1-9.
  7. Kelly, S. E. (1996), “Gibbs phenomenon for wavelets”, Appl. Comp. Harmon. Anal., Vol. 3, pp. 7281.
  8. Kelly, S. E., Kon, M.A. and Raphael, L.A. (1994), Local Convergence for Wavelet Expansions, J. Funct. Anal., 126, pp. 102138.
  9. Mallat, S. (1999), “A Wavelet Tour of Signal Processing”, Cambridge University Press, London.
  10. Walter, G. and Shen, X. (1998), “Positive estimation with wavelets, in Wavelets, Multiwavelets and their Applications”, Contemporary Mathematics, Aldroubi and Lin, eds., Vol. 216, AMS, Providence RI, pp. 6379.
  11. Toeplitz, O. (1911), “ uber all gemeine lineare Mittelbuildungen”, Press Mathematyezno Fizyezne, 22, 113-119.
  12. Dhakal, B. P. (2010), “Approximation of Functions Belonging to the Lip Class by Matrix-Cesaro Summability Method”, International Mathematical Forum, Vol. 5, no. 35, pp. 1729-1735.
  13. Norlund, N. E. (1919), “Surune application des functions permutables”, Lund. Universitets Arsskrift, 16, 1-10.
  14. Borwein, D. (1958), “On Product of Sequences”, Jour. London Math. Soc., 33, 352-357.
  15. Askey, R. (1972), “Jacobi summability”, J. Approx. Theory, 5, pp. 387-392.
  16. Cohen, A. (2003), “Numerical Analysis of Wavelets Methods”, Studies in Mathematics and its Applications, Vol. 32, North-Holland, Elsevier, Amsterdam.
  17. Daubechies, I. (1992), “Ten Lectures on Wavelets”, SIAM, Philadelphia.
  18. Keinert, F. (2004), “Wavelets and Multiwavelets”, Chapman & Hall/CRC, Florida.
  19. Shim, H. T. and Volkmer, H. (1996), “On the Gibbs Phenomenon for Wavelet Expansions”, J. Approx. Theory 84, pp. 74-95.
Index Terms

Computer Science
Information Sciences

Keywords

Jacobi orthogonal polynomials matrix-Cesaro (Λ⋅C 1 ) method of Jacobi polynomials (N p n )⋅C 1 method multiresolution analysis orthogonal projection the Gibbs phenomenon in wavelet analysis.

Powered by PhDFocusTM