• Corpus ID: 204838215

Adaptive Padé-Chebyshev Type Approximation to Piecewise Smooth Functions

  title={Adaptive Pad{\'e}-Chebyshev Type Approximation to Piecewise Smooth Functions},
  author={Sharma Akansha and Sambandam Baskar},
The aim of this article is to study the role of piecewise implementation of Pade-Chebyshev type approximation in minimising Gibbs phenomena in approximating piecewise smooth functions. A piecewise Pade-Chebyshev type (PiPCT) algorithm is proposed and an $L^1$-error estimate for at most continuous functions is obtained using a decay property of the Chebyshev coefficients. An advantage of the PiPCT approximation is that we do not need to have an {\it a prior} knowledge of the positions and the… 
Piecewise Pad\'e-Chebyshev Reconstruction of Bivariate Piecewise Smooth Functions
  • A. Singh
  • Mathematics, Computer Science
  • 2021
This article aims to implement the novel piecewise Maehly based Padé-Chebyshev approximation, developing a method referred to as PiPC to approximate univariate piecewise smooth functions and then extending the same to a two-dimensional space, leading to a bivariate piece wise Pader-Chebyv approximation (Pi2DPC) for approximating piecewise smoother functions in two-dimension.


Approximating piecewise-smooth functions
We consider the possibility of using locally supported quasi-interpolation operators for the approximation of univariate nonsmooth functions. In such a case, one usually expects the rate of
Approximating the jump discontinuities of a function by its Fourier-Jacobi coefficients
This paper generalizes Eckhoff's method for approximating the locations of discontinuities and the associated jumps of a piecewise smooth function by means of its Fourier-Chebyshev coefficients and studies the accuracy of the approximations.
Nonlinear approximation
This is a survey of nonlinear approximation, especially that part of the subject which is important in numerical computation. Nonlinear approximation means that the approximants do not come from
Nonlinear Methods in Numerical Analysis
I. Continued Fractions. Since these play an important role, the first chapter introduces their basic properties, evaluation algorithms and convergence theorems. From the section dealing with
Exponentially Accurate Approximations to Periodic Lipschitz Functions Based on Fourier Series Partial Sums
2π-periodic function f and its first few derivatives, given only a truncated Fourier series representation of f, is studied and solved and it is shown that these new approximations, and their derivatives, converge exponentially in the maximum norm to f, and its corresponding derivatives, except in the union of a finite number of small open intervals.
Accurate reconstruction of discontinuous functions using the singular pade-chebyshev method
In this paper, we present a singularity-based resolution of the Gibbs phenomenon that obstructs the reconstruction of a function with jump discontinuities by a truncated Chebyshev series or a
Fourier-Padé approximations and filtering for spectral simulations of an incompressible Boussinesq convection problem
Rational approximations based on Fourier series representation are presented and it is shown that those methods converge exponentially in the smooth region and successfully reduce the Gibbs oscillations as the degrees of the denominators and the numerators of the Pade approximants increase.
Interpolation and Approximation of Piecewise Smooth Functions
It is proved that in the presence of isolated singularities, the approximation order provided by the interpolation procedure is improved by a factor of $h$ relative to the linear methods, where h is the sampling rate.
A Padé-based algorithm for overcoming the Gibbs phenomenon
The standard Fourier–Padé approximation, which is known to improve on the convergence of partial summation in the case of periodic, globally analytic functions, is here extended to functions with jumps to exhibit exponential convergence globally for piecewise analytic functions when the jump location(s) are known.
Accurate reconstructions of functions of finite regularity from truncated Fourier series expansions
Kowledge of a truncated Fourier series expansion for a 2π-periodic function of finite regularity, which is assumed to be piecewise smooth in each period, is used to accurately reconstruct the