Results 1 to 10 of about 1,854 (206)

Lebesgue functions and Lebesgue constants in polynomial interpolation [PDF]

Journal of Inequalities and Applications, 2016
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.
Bayram Ali Ibrahimoglu
doaj   +5 more sources

On Lebesgue Constants

Axioms
Simple formulae for Lebesgue constants arising in the classical Fourier series approximation are obtained. Both even and odd cases are addressed, extending Fejér’s results. Asymptotic formulae are also obtained.
Manuel Duarte Ortigueira, Gabriel Bengochea   +1 more
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Upper Bound for Lebesgue Constant of Bivariate Lagrange Interpolation Polynomial on the Second Kind Chebyshev Points

Journal of Mathematics, 2022
In the paper, we study the upper bound estimation of the Lebesgue constant of the bivariate Lagrange interpolation polynomial based on the common zeros of product Chebyshev polynomials of the second kind on the square −1,12. And, we prove that the growth
Juan Liu, Laiyi Zhu
doaj   +1 more source

Node Generation for RBF-FD Methods by QR Factorization

Mathematics, 2021
Polyharmonic spline (PHS) radial basis functions (RBFs) have been used in conjunction with polynomials to create RBF finite-difference (RBF-FD) methods. In 2D, these methods are usually implemented with Cartesian nodes, hexagonal nodes, or most commonly,
Tony Liu, Rodrigo B. Platte
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Sharp Estimates for Lebesgue Constants [PDF]

Proceedings of the American Mathematical Society, 1983
Suppose C ⊂ R N C \subset {R^N} is a closed convex bounded body containing 0 in its interior. If ∂ C \partial C is sufficiently smooth with strictly positive Gauss curvature at each point, then, denoting by
Carenini, M, SOARDI, PAOLO MAURIZIO
openaire   +2 more sources

Decision problems for linear recurrences involving arbitrary real numbers [PDF]

Logical Methods in Computer Science, 2021
We study the decidability of the Skolem Problem, the Positivity Problem, and the Ultimate Positivity Problem for linear recurrences with real number initial values and real number coefficients in the bit-model of real computation.
Eike Neumann
doaj   +1 more source

Lebesgue Constant Using Sinc Points [PDF]

Advances in Numerical Analysis, 2016
Lebesgue constant for Lagrange approximation at Sinc points will be examined. We introduce a new barycentric form for Lagrange approximation at Sinc points. Using Thiele’s algorithm we show that the Lebesgue constant grows logarithmically as the number of interpolation Sinc points increases.
Maha Youssef, Hany A. El-Sharkawy, Gerd Baumann   +2 more
openaire   +2 more sources

On measure of noncompactness in variable exponent Lebesgue spaces and applications to integral equations

Journal of Inequalities and Applications, 2023
A novel measure of noncompactness is defined in variable exponent Lebesgue spaces L p ( ⋅ ) $L^{p(\cdot )}$ on an unbounded domain R + $\mathbb{R}^{+}$ and its properties are examined.
Mohamed M. A. Metwali
doaj   +1 more source

Almost Optimality of the Orthogonal Super Greedy Algorithm for μ-Coherent Dictionaries

Axioms, 2022
We study the approximation capability of the orthogonal super greedy algorithm (OSGA) with respect to μ-coherent dictionaries in Hilbert spaces. We establish the Lebesgue-type inequalities for OSGA, which show that the OSGA provides an almost optimal ...
Chunfang Shao, Jincai Chang, Peixin Ye, Wenhui Zhang, Shuo Xing   +4 more
doaj   +1 more source

Endpoint Estimates for a Class of Littlewood-Paley Operators with Nondoubling Measures

Journal of Inequalities and Applications, 2009
Let μ be a positive Radon measure on ℝd which may be nondoubling. The only condition that μ satisfies is μ(B(x,r))≤C0rn for all x∈ℝd, r>0, and some fixed constant C0. In this paper, we introduce the
Qingying Xue, Juyang Zhang
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