A note on the perturbed trapezoid inequality.
A note on the rate of convergence for Chebyshev-Lobatto and Radau systems
This paper is devoted to Hermite interpolation with Chebyshev-Lobatto and Chebyshev-Radau nodal points. The aim of this piece of work is to establish the rate of convergence for some types of smooth functions. Although the rate of convergence is similar to that of Lagrange interpolation, taking into account the asymptotic constants that we obtain, the use of this method is justified and it is very suitable when we dispose of the appropriate information.
A note on the sharpness of the Remez-type inequality for homogeneous polynomials on the sphere.
A parallel algorithm for discrete least squares rational approximation.
A particular smooth interpolation that generates splines
There are two grounds the spline theory stems from - the algebraic one (where splines are understood as piecewise smooth functions satisfying some continuity conditions) and the variational one (where splines are obtained via minimization of some quadratic functionals with constraints). We use the general variational approach called smooth interpolation introduced by Talmi and Gilat and show that it covers not only the cubic spline and its 2D and 3D analogues but also the well known tension spline...
A pointwise approximation theorem for linear combinations of Bernstein polynomials.
A powerful determinant.
A priori convergence of the greedy algorithm for the parametrized reduced basis method
The convergence and efficiency of the reduced basis method used for the approximation of the solutions to a class of problems written as a parametrized PDE depends heavily on the choice of the elements that constitute the “reduced basis”. The purpose of this paper is to analyze the a priori convergence for one of the approaches used for the selection of these elements, the greedy algorithm. Under natural hypothesis on the set of all solutions to the problem obtained when the parameter varies, we...
A priori convergence of the Greedy algorithm for the parametrized reduced basis method
The convergence and efficiency of the reduced basis method used for the approximation of the solutions to a class of problems written as a parametrized PDE depends heavily on the choice of the elements that constitute the “reduced basis”. The purpose of this paper is to analyze the a priori convergence for one of the approaches used for the selection of these elements, the greedy algorithm. Under natural hypothesis on the set of all solutions to the problem obtained when the parameter varies, we...
A priori convergence of the Greedy algorithm for the parametrized reduced basis method
The convergence and efficiency of the reduced basis method used for the approximation of the solutions to a class of problems written as a parametrized PDE depends heavily on the choice of the elements that constitute the “reduced basis”. The purpose of this paper is to analyze the a priori convergence for one of the approaches used for the selection of these elements, the greedy algorithm. Under natural hypothesis on the set of all solutions to the problem obtained when the parameter varies, we...
A probabilistic approach to representation formulae for semigroups of operators with rates of convergence.
A Probabilistic Theory for Error Estimation in Automatic Integration.
A proof of Leibniz's formula for divided differences.
A quadrature formula of rational type for integrands with one endpoint singularity.
A recursive interpolation method in
A remark on a class of universal hill functions
A remark on a modified Szász-Mirakjan operator
We prove that, for a sequence of positive numbers δ(n), if as , to guarantee that the modified Szász-Mirakjan operators converge to f(x) at every point, f must be identically zero.
A remark on a theorem of A. B. Németh regarding the convergence of sequences of linear operators on space C[a,b]
A Remark on Periodic Tchebyshev Systems.
A remark on the approximation theorems of Whitney and Carleman-Scheinberg
We show that a -smooth mapping on an open subset of , , can be approximated in a fine topology and together with its derivatives by a restriction of a holomorphic mapping with explicitly described domain. As a corollary we obtain a generalisation of the Carleman-Scheinberg theorem on approximation by entire functions.