A New Strategy for Choosing the Chebyshev-Gegenbauer Parameters in a Reconstruction Based on Asymptotic Analysis
Journal Title: Mathematical Modelling and Analysis - Year 2010, Vol 15, Issue 2
Abstract
The Gegenbauer reconstruction method, first proposed by Gottlieb et. al. in 1992, has been considered a useful technique for re-expanding finite series polynomial approximations while simultaneously avoiding Gibbs artifacts. Since its introduction many studies have analyzed the method's strengths and weaknesses as well as suggesting several applications. However, until recently no attempts were made to optimize the reconstruction parameters, whose careful selection can make the difference between spectral accuracies and divergent error bounds. In this paper we propose asymptotic analysis as a method for locating the optimal Gegenbauer reconstruction parameters. Such parameters are useful to applications of this reconstruction method that either seek to bound the number of Gegenbauer expansion coefficients or to control compression ratios. We then illustrate the effectiveness of our approach with the results from some numerical experiments.
Authors and Affiliations
Z. Jackiewicz, R. Park
Keywords
Related Articles
- EP ID EP84788
- DOI 10.3846/1392-6292.2010.15.199-22
- Views 61
- Downloads 0
Construction of Chaotic Dynamical System
The first-order difference equation x[i][sub]n[/sub][/i][sub]+1[/sub] = [i]f [/i](x[i][sub]n[/sub][/i]),[i] n[/i] = 0, 1, . . ., where [i]f[/i] : R → R, is referred as an one-dimensional discrete dynamical system. If fun...
A New Strategy for Choosing the Chebyshev-Gegenbauer Parameters in a Reconstruction Based on Asymptotic Analysis
The Gegenbauer reconstruction method, first proposed by Gottlieb et. al. in 1992, has been considered a useful technique for re-expanding finite series polynomial approximations while simultaneously avoiding Gibbs artifa...
Positive Solutions Bifurcating from Zero Solution in a Predator-Prey Reaction–Diffusion System
An elliptic system subject to the homogeneous Dirichlet boundary con- dition denoting the steady-state system of a two-species predator-prey reaction– diffusion system with the modified Leslie–Gower and Holling-type II s...
Identification of Microstructured Materials by Phase and Group Velocities
An inverse problem to determine parameters of microstructured solids by means of group and phase velocities of wave packets is studied. It is proved that in the case of normal dispersion the physical solution is unique a...
Numerical Study of the Rosensweig Instability in a Magnetic Fluid Subject to Diffusion of Magnetic Particles
The present study is devoted to the classical problem on stability of a magnetic fluid layer under the influence of gravity and a uniform magnetic field. A periodical peak-shaped stable structure is formed on the fluid s...