Perturbations of an Ostrowski type inequality and applications.
Perturbations of Best Approximation Problems.
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,...
Piecewise atone interpolation of monotone operators
Piecewise L-Splines.
Piecewise Polynomial Spaces and Geometric Continuity of Curves.
Point derivations and prime ideals in R(X)
Points minimaux dans les espaces de Banach
Points minimaux dans les espaces de Banach (suite)
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 convergence for expansions in surface harmonics of arbitrary dimension.
Pointwise estimates for modified positive linear operators
Pointwise inequalities and approximation in fractional Sobolev spaces
We prove that a function belonging to a fractional Sobolev space may be approximated in capacity and norm by smooth functions belonging to , 0 < m + λ < α. Our results generalize and extend those of [12], [4], [14], and [11].
Pointwise inequalities for Sobolev functions and some applications
We get a class of pointwise inequalities for Sobolev functions. As a corollary we obtain a short proof of Michael-Ziemer’s theorem which states that Sobolev functions can be approximated by functions both in norm and capacity.
Pointwise Rational Approximation and Iterative Methods for Ill-Posed Problems.
Polinomios ortogonales asociados con problemas espectrales
Polya conditions for multivariate Birkhoff interpolation: from general to rectangular sets of nodes.
Pólya Operators I: Total Positivity.
Pólya Operators II: Complete Concavity.
Polyharmonic homogenization, rough polyharmonic splines and sparse super-localization
We introduce a new variational method for the numerical homogenization of divergence form elliptic, parabolic and hyperbolic equations with arbitrary rough (L∞) coefficients. Our method does not rely on concepts of ergodicity or scale-separation but on compactness properties of the solution space and a new variational approach to homogenization. The approximation space is generated by an interpolation basis (over scattered points forming a mesh of resolution H) minimizing the L2 norm of the source...