Algebraic Polynomial Approximation
In this chapter we relate the rate of convergence of best polynomial approximation to our new modulus of smoothness. Asymptotic behavior of the derivatives of the optimal algebraic polynomials will also be related to that modulus of smoothness. The results are of both direct and converse type and yield necessary and sufficient conditions whenever the rate of best approximation is n−α for instance.
KeywordsError Bound Polynomial Approximation Trigonometric Polynomial Gaussian Quadrature Classical Modulus
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