Lebesgue Constants for an Orthogonal Polynomial Schauder Basis
نویسندگان
چکیده
We examine a certain class of Schauder bases for the space C[−1, 1] consisting of algebraic polynomials orthogonal with respect to the Chebycheff weight of the first kind. We give an improved estimate for its Lebesgue constants.
منابع مشابه
Polynomial Schauder basis of optimal degree with Jacobi orthogonality
In our paper we construct a polynomial Schauder basis (pα,β,n)n∈N0 of optimal degree with Jacobi orthogonality. A candidate for such a basis is given by the use of some wavelet theoretical methods, which were already successful in case of Tchebysheff and Legendre orthogonality. To prove that this sequence is in fact a Schauder basis for C[−1, 1] and as the main difficulty of the whole proof we ...
متن کاملLebesgue Constants and Optimal Node Systems via Symbolic Computations
Polynomial interpolation is a classical method to approximate continuous functions by polynomials. To measure the correctness of the approximation, Lebesgue constants are introduced. For a given node system X = {x1 < . . . < xn+1} (xj ∈ [a, b]), the Lebesgue function λn(x) is the sum of the modulus of the Lagrange basis polynomials built on X. The Lebesgue constant Λn assigned to the function λ...
متن کاملLebesgue functions and Lebesgue constants in polynomial interpolation
The Lebesgue constant is a valuable numerical instrument for linear interpolation because it provides a measure of how close the interpolant of a function is to the best polynomial approximant of the function. Moreover, if the interpolant is computed by using the Lagrange basis, then the Lebesgue constant also expresses the conditioning of the interpolation problem. In addition, many publicatio...
متن کاملCharacterization of Local Besov Spaces via Wavelet Basis Expansions
In this paper we deal with local Besov spaces of periodic functions of one variable. We characterize these spaces in terms of summability conditions on the coefficients in series expansions of their elements with respect to an orthogonal Schauder basis of trigonometric polynomials. We consider a Schauder basis that was constructed by using ideas of a periodic multiresolution analysis and corres...
متن کاملLebesgue constants in polynomial interpolation
Lagrange interpolation is a classical method for approximating a continuous function by a polynomial that agrees with the function at a number of chosen points (the “nodes”). However, the accuracy of the approximation is greatly influenced by the location of these nodes. Now, a useful way to measure a given set of nodes to determine whether its Lagrange polynomials are likely to provide good ap...
متن کامل