# Adaptive Padé-Chebyshev Type Approximation to Piecewise Smooth Functions

@article{Akansha2019AdaptivePT, title={Adaptive Pad{\'e}-Chebyshev Type Approximation to Piecewise Smooth Functions}, author={Sharma Akansha and Sambandam Baskar}, journal={ArXiv}, year={2019}, volume={abs/2110.07173} }

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…

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Piecewise Pad\'e-Chebyshev Reconstruction of Bivariate Piecewise Smooth Functions

- 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.

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