Error bounds for Gauss-Lobatto quadrature formula with multiple end points with Chebyshev weight function of the third and the fourth kind

An Error Expansion for Gauss–Turán Quadrature with Chebyshev Weight Function

Our aim in this paper is to obtain an expansion for the error in the Gauss-Turán quadrature formula for approximating ∫ 1 −1 w(t)f(t) dt in the case when the function f is analytic in some region of the complex plane containing the interval [−1, 1] in its interior, and the remainder term is presented in the form of a contour integral over the confocal ellipses. In the case w(t) = 1/ √ 1 − t2 we...

the evaluation of language related engagment and task related engagment with the purpose of investigating the effect of metatalk and task typology

abstract while task-based instruction is considered as the most effective way to learn a language in the related literature, it is oversimplified on various grounds. different variables may affect how students are engaged with not only the language but also with the task itself. the present study was conducted to investigate language and task related engagement on the basis of the task typolog...

Error Bounds for Gauss-kronrod Quadrature Formulae

The Gauss-Kronrod quadrature formula Qi//+X is used for a practical estimate of the error R^j of an approximate integration using the Gaussian quadrature formula Q% . Studying an often-used theoretical quality measure, for ߣ* , we prove best presently known bounds for the error constants cs(RTMx)= sup \RlK+x[f]\ ll/(l»lloo<l in the case s = "Sn + 2 + tc , k = L^J LfJ • A comparison with the Ga...

Asymptotic Error Estimates for the Gauss Quadrature Formula

Vandermonde systems on Gauss-Lobatto Chebyshev nodes

This paper deals with Vandermonde matrices Vn whose nodes are the Gauss–Lobatto Chebyshev nodes, also called extrema Chebyshev nodes. We give an analytic factorization and explicit formula for the entries of their inverse, and explore its computational issues. We also give asymptotic estimates of the Frobenius norm of both Vn and its inverse and present an explicit formula for the determinant o...