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

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

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

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

scholarly journals How much faster does the best polynomial approximation converge than Legendre projection?

2021 ◽  
Vol 147 (2) ◽  
pp. 481-503
Author(s):  
Haiyong Wang
Keyword(s):  
Polynomial Approximation ◽  
Best Polynomial Approximation
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