Permanence de relations de récurrence dans certains développements asymptotiques. (Permanence of recurrence relations in certain asymptotic expansions).
Piecewise approximation and neural networks
The paper deals with the recently proposed autotracking piecewise cubic approximation (APCA) based on the discrete projective transformation, and neural networks (NN). The suggested new approach facilitates the analysis of data with complex dependence and relatively small errors. We introduce a new representation of polynomials that can provide different local approximation models. We demonstrate how APCA can be applied to especially noisy data thanks to NN and local estimations. On the other hand,...
Pointwise approximation by Meyer-König and Zeller operators
We study the rate of pointwise convergence of Meyer-König and Zeller operators for bounded functions, and get an asymptotically optimal estimate.
Pointwise estimates for modified positive linear operators
Polynomial approximation and the quadrature problem over a semi-infinite interval
Polynomial approximation and twenty years later.
Polynomial approximation of differentiable functions on Banach spaces.
Polynomial asymptotics and approximation of Sobolev functions
We prove several results concerning density of , behaviour at infinity and integral representations for elements of the space .
Polynomial best constrained degree reduction in strain energy.
Polynomial chaos in evaluating failure probability: A comparative study
Recent developments in the field of stochastic mechanics and particularly regarding the stochastic finite element method allow to model uncertain behaviours for more complex engineering structures. In reliability analysis, polynomial chaos expansion is a useful tool because it helps to avoid thousands of time-consuming finite element model simulations for structures with uncertain parameters. The aim of this paper is to review and compare available techniques for both the construction of polynomial...
Polynomial inequalities, functional spaces and best approximation on the real semiaxis with Laguerre weights.
Polynomial inequalities on general subsets of
Polynomial two-point expansions.
Přímý důkaz průkladného vzorce Lagrange-ova
Problème de Bernstein pour les fonctions différentiables
Projections in uniform polynomial approximations
Properties of the modulus of continuity for monotonous convex functions and applications.
Quasianalytic functions in the sense of Bernstein [Book]
Quasiconvex functions can be approximated by quasiconvex polynomials
Let W be a function from the real m×n-matrices to the real numbers. If W is quasiconvex in the sense of the calculus of variations, then we show that W can be approximated locally uniformly by quasiconvex polynomials.
Reference points based recursive approximation
The paper studies polynomial approximation models with a new type of constraints that enable to get estimates with significant properties. Recently we enhanced a representation of polynomials based on three reference points. Here we propose a two-part cubic smoothing scheme that leverages this representation. The presence of these points in the model has several consequences. The most important one is the fact that by appropriate location of the reference points the resulting approximant of two...