2021/10/14 by S. Akansha, Akansha, S., S. Baskar +1
Computer Science · Decision Sciences · Mathematics · #41A21 #41A25 #65D15 #FOS: Mathematics #Image and Signal Denoising Methods #Iterative Methods for Nonlinear Equations #Numerical Analysis (math.NA) #Probabilistic and Robust Engineering Design
paper · pdf · doi:10.48550/arxiv.2110.07173
openalex publication_date 2021/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A piecewise Padé-Chebyshev type (PiPCT) approximation method is proposed to minimize the Gibbs phenomenon in approximating piecewise smooth functions. A theorem on L1-error estimate is proved for sufficiently smooth functions using a decay property of the Chebyshev coefficients. Numerical experiments are performed to show that the PiPCT method accurately captures isolated singularities of a function without using the positions and the types of singularities. Further, an adaptive partition approach to the PiPCT method is developed (referred to as the APiPCT method) to achieve the required accuracy with a lesser computational cost. Numerical experiments are performed to show some advantages of using the PiPCT and APiPCT methods compared to some well-known methods in the literature.