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

Shyam Lal, Manoj Kumar
2016 International Journal of Computer Applications  
In this paper, an application to the approximation by wavelets has been obtained by using matrix-Cesàro (Λ · C 1 ) method of Jacobi polynomials. The rapid rate of convergence of matrix-Cesàro 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
more » ... ns. The matrix-Cesàro (Λ·C 1 ) method includes (N, p n )·C 1 method as a particular case. The comparison between the numerical results obtained by the (N, p n ) · C 1 and matrix-Cesàro (Λ · C 1 ) summability method reveals a slight improvement concerning the reduction of the excessive oscillations by using the approach of present paper. General Terms Summability methods, Jacobi polynomials, wavelet expansions, wavelet approximation, projection, the Gibbs phenomenon in wavelet analysis. Keywords Jacobi orthogonal polynomials, matrix-Cesàro (Λ · C 1 ) method of Jacobi polynomials, (N, p n )·C 1 method, multiresolution analysis, orthogonal projection, the Gibbs phenomenon in wavelet analysis.
doi:10.5120/ijca2016911210 fatcat:4v63eddi2rhspbjrk4plhqo6va