The Gibbs phenomenon for bestL 1-trigonometric polynomial approximation

1995 ◽  
Vol 11 (3) ◽  
pp. 391-416 ◽  
Author(s):  
E. Moskona ◽  
P. Petrushev ◽  
E. B. Saff
Keyword(s):  
Trigonometric Polynomial ◽  
Polynomial Approximation ◽  
Gibbs Phenomenon ◽  
Trigonometric Polynomial Approximation

Trigonometric polynomial approximation in theL 1-norm

1979 ◽  
Vol 169 (3) ◽  
pp. 261-269 ◽  
Author(s):  
Franz Peherstorfer
Keyword(s):  
Trigonometric Polynomial ◽  
Polynomial Approximation ◽  
Trigonometric Polynomial Approximation

scholarly journals Polynomial approximation on spheres - generalizing de la Vallée-Poussin

2011 ◽  
Vol 11 (4) ◽  
pp. 540-552 ◽  
Author(s):  
Ian H. Sloan
Keyword(s):  
Trigonometric Polynomial ◽  
Polynomial Approximation ◽  
Piecewise Linear ◽  
Continuous Functions ◽  
Fast Convergence ◽  
Piecewise Polynomial ◽  
Smooth Functions ◽  
Higher Dimensional ◽  
Trigonometric Polynomial Approximation ◽  
De La Vallée Poussin

AbstractFor trigonometric polynomial approximation on a circle, the century-old de la Vallée-Poussin construction has attractive features: it exhibits uniform convergence for all continuous functions as the degree of the trigonometric polynomial goes to infinity, yet it also has arbitrarily fast convergence for sufficiently smooth functions. This paper presents an explicit generalization of the de la Vallée-Poussin construction to higher dimensional spheres S^d ≤ R^{d+1}. The generalization replaces the C^∞ filter introduced by Rustamov by a piecewise polynomial of minimal degree. For the case of the circle the filter is piecewise linear, and recovers the de la Vallée-Poussin construction, while for the general sphere S^d the filter is a piecewise polynomial of degree d and smoothness C^{d−1}. In all cases the approximation converges uniformly for all continuous functions, and has arbitrarily fast convergence for smooth functions.

scholarly journals Nonperiodic Trigonometric Polynomial Approximation

2013 ◽  
Vol 60 (2) ◽  
pp. 345-362 ◽  
Author(s):  
Hillel Tal-Ezer
Keyword(s):  
Trigonometric Polynomial ◽  
Polynomial Approximation ◽  
Trigonometric Polynomial Approximation

Trigonometric polynomial approximation

2009 ◽  
pp. 19-42
Author(s):  
Jan S. Hesthaven ◽  
Sigal Gottlieb ◽  
David Gottlieb
Keyword(s):  
Trigonometric Polynomial ◽  
Polynomial Approximation ◽  
Trigonometric Polynomial Approximation

Optimization of Neural Network Training for Image Recognition Based on Trigonometric Polynomial Approximation

2021 ◽  
Vol 47 (8) ◽  
pp. 830-838
Author(s):  
N. Vershkov ◽  
M. Babenko ◽  
A. Tchernykh ◽  
B. Pulido-Gaytan ◽  
J. M. Cortés-Mendoza ◽  
...  
Keyword(s):  
Neural Network ◽  
Trigonometric Polynomial ◽  
Image Recognition ◽  
Polynomial Approximation ◽  
Neural Network Training ◽  
Network Training ◽  
Trigonometric Polynomial Approximation

Investigation of discontinuous periodic signals using the measuring labview complex

2020 ◽  
pp. 72-79
Author(s):  
E.B. Solovyeva ◽  
◽  
Yu.M. Inshakov ◽  
Keyword(s):  
Fourier Series ◽  
Laboratory Experiment ◽  
Gibbs Phenomenon ◽  
Electrical Signals ◽  
Measuring Complex ◽  
Universal Measuring ◽  
Depth Study ◽  
Periodic Signals ◽  
Truncated Fourier Series

General approaches to the analysis of the Gibbs phenomenon for discontinuous periodic signals approximated by the truncated Fourier series are considered. Methods for smoothing the truncated Fourier series and improving its convergence are discussed. The software means for modeling is a universal measuring complex LabVIEW, which possesses a convenient environment for analyzing electrical signals, on the basis of this complex a laboratory experiment is carried out. The advantages of the measuring LabVIEW complex and its capabilities for in-depth study of discontinuous periodic signals are noted.

Nonlinear Piecewise Polynomial Approximation Beyond Besov Spaces

2001 ◽  
Author(s):  
Borislav Karaivanov ◽  
Pencho Petrushev
Keyword(s):  
Polynomial Approximation ◽  
Besov Spaces ◽  
Piecewise Polynomial ◽  
Piecewise Polynomial Approximation
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