Determination of the algebraic polynomial of best approximation

Cybernetics ◽  
1969 ◽  
Vol 5 (5) ◽  
pp. 676-682 ◽  
Author(s):  
V. N. Malozemov
Keyword(s):  
Best Approximation ◽  
Algebraic Polynomial ◽  
Polynomial Of Best Approximation

scholarly journals Polynomial of Best Uniform Approximation to and Smoothing in Two-level Methods

2012 ◽  
Vol 12 (4) ◽  
pp. 448-468 ◽  
Author(s):  
Johannes Kraus ◽  
Panayot Vassilevski ◽  
Ludmil Zikatanov
Keyword(s):  
Best Approximation ◽  
Finite Interval ◽  
Elliptic Partial Differential Equation ◽  
Uniform Norm ◽  
Defect Correction ◽  
Fine Grid ◽  
Smoothing Property ◽  
Correction Scheme ◽  
Polynomial Of Best Approximation ◽  
Level Method

AbstractWe derive defect correction scheme for constructing the sequence of polynomials of best approximation in the uniform norm to 1/x on a finite interval with positive endpoints. As an application, we consider two-level methods for scalar elliptic partial differential equation (PDE), where the relaxation on the fine grid uses the aforementioned polynomial of best approximation. Based on a new smoothing property of this polynomial smoother that we prove, combined with a proper choice of the coarse space, we obtain as a corollary, that the convergence rate of the resulting two-level method is uniform with respect to the mesh parameters, coarsening ratio and PDE coefficient variation.

scholarly journals Derivatives of a polynomial of best approximation and modulus of smoothness in generalized Lebesgue spaces with variable exponent

2017 ◽  
Vol 50 (1) ◽  
pp. 245-251 ◽  
Author(s):  
Sadulla Z. Jafarov
Keyword(s):  
Best Approximation ◽  
Variable Exponent ◽  
Modulus Of Smoothness ◽  
Lebesgue Spaces ◽  
The Best Approximation ◽  
Polynomial Of Best Approximation ◽  
The Relationship ◽  
Derivatives Of ◽  
De La Vallée Poussin

Abstract The relation between derivatives of a polynomial of best approximation and the best approximation of the function is investigated in generalized Lebesgue spaces with variable exponent. In addition, the relationship between the fractional modulus of smoothness of the function and its de la Vallée-Poussin sums is studied.

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