Related papers: Stability Analysis of Gr\"unwald Interpolation Ope…
In this paper, we introduce a new sequence of operators based on the Gr\"unwald interpolation operators on Chebyshev nodes on the space $L^p[0,{\pi}]$. The operators we consider are integral variants of the Gr\"unwald interpolation…
In this paper, we construct a Durrmeyer-type variant of Gr\"unwald interpolation operators on the space $L^p[0,{\pi}]$. We prove their fundamental properties, including boundedness and convergence in the $L^p$-norm. We establish the…
The paper deals with a special filtered approximation method, which originates interpolation polynomials at Chebyshev zeros by using de la Vall\'ee Poussin filters. These polynomials can be an useful device for many theoretical and…
We consider weighted uniform convergence of entire analogues of the Gr\"unwald operator on the real line. The main result deals with convergence of entire interpolations of exponential type $\tau>0$ at zeros of Bessel functions in spaces…
We show that interpolation results in the $S$-nodes theory may be considered as Khrushchev-type formulas. If separation of the well-known Verblunsky (Schur) coefficients occurs in Khrushchev formulas, the separation of the so the called new…
In order to solve Prandtl-type equations we propose a collocation-quadrature method based on VP filtered interpolation at Chebyshev nodes. Uniform convergence and stability are proved in a couple of Holder - Zygmund spaces of locally…
The present paper concerns filtered de la Vall\'ee Poussin (VP) interpolation at the Chebyshev nodes of the four kinds. This approximation model is interesting for applications because it combines the advantages of the classical Lagrange…
We prove the stability of isomorphisms between Banach spaces generated by interpolation methods introduced by Cwikel-Kalton-Milman-Rochberg which includes, as special cases, the real and complex methods up to equivalence of norms and also…
The purpose of this paper is to introduce the class of enriched interpolative Kannan type operators on Banach space that contains the classes of enriched Kannan operators, interpolative Kannan type contraction operators and some other…
The study is made of the problem of multiple interpolation on an infinite nodes set by the sums of absolutely convergent series of exponentials whose exponents are from a given set. For entire function conditions on nodes and exponents are…
Chebyshev interpolation is a highly effective, intensively studied method and enjoys excellent numerical properties. The interpolation nodes are known beforehand, implementation is straightforward and the method is numerically stable. For…
This work develops a computational framework for proving existence, uniqueness, isolation, and stability results for real analytic fixed points of $m$-th order Feigenbaum-Cvitanovi\'{c} renormalization operators. Our approach builds on the…
In convergence analysis of finite element methods for singularly perturbed reaction--diffusion problems, balanced norms have been successfully introduced to replace standard energy norms so that layers can be captured. In this article, we…
Block-to-block interface interpolation operators are constructed for several common high-order finite difference discretizations. In contrast to conventional interpolation operators, these new interpolation operators maintain the strict…
The classical Korovkin theorem traditionally relies on the positivity of the underlying sequence of operators. However, in 1968, D. E. Wulbert established the first non-positive version. In this article, we generalize Wulbert's result to…
We give the connections among the Fekete sets, the zeros of orthogonal polynomials, $1(w)$-normal point systems, and the nodes of a stable and most economical interpolatory process via the Fej\'er contants. Finally the convergence of a…
We consider interpolation of univariate functions on arbitrary sets of nodes by Gaussian radial basis functions or by exponential functions. We derive closed-form expressions for the interpolation error based on the…
In this paper, we present recent stability results with explicit and dimensionally sharp constants and optimal norms for the Sobolev inequality and for the Gaussian logarithmic Sobolev inequality obtained by the authors in [24]. The…
We show that for integral operators of general form the norm bounds in Lorentz spaces imply certain norm bounds for the maximal function. As a consequence, the a.e. convergence for the integral operators on the Lorentz spaces follows from…
We present a new analysis of the stability of the first and second barycentric formulae for interpolation at the Chebyshev points of the second kind. Our theory shows that the second formula is more stable than previously thought and our…