Related papers: Average Interpolation Under the Maximum Angle Cond…
The convergence rates on polynomial interpolation in most cases are estimated by Lebesgue constants. These estimates may be overestimated for some special points of sets for functions of limited regularities. In this paper, by applying the…
In this paper we introduce a class of BMO spaces which interpolate with $L_p$ and are sufficiently large to serve as endpoints for new singular integral operators. More precisely, let $(\Omega, \Sigma, \mu)$ be a $\sigma$-finite measure…
In non-private stochastic convex optimization, stochastic gradient methods converge much faster on interpolation problems -- problems where there exists a solution that simultaneously minimizes all of the sample losses -- than on…
Traditional measures of smoothness often fail to provide accurate $L_p$-error estimates for approximation by sampling or interpolation operators, especially for functions with low smoothness. To address this issue, we introduce a modified…
We introduce interpolation operators with approximation and stability properties suited for parabolic problems in primal and mixed formulations. We derive localized error estimates for tensor product meshes (occurring in classical…
We study the delay margin problem in the context of recent works by T. Qi, J. Zhu, and J. Chen, where a sufficient condition for the maximal delay margin is formulated in terms of an interpolation problem obtained after introducing a…
The problem of the mean-square optimal linear estimation of linear functionals which depend on the unknown values of a multidimensional continuous time stationary stochastic process is considered. Estimates are based on observations of the…
This paper gives a general interpretation of Linear Prediction (LP) by interpolation framework different from the perspective of statistics. This interpretation is proved to be useful by several following results, such as: The mechanism of…
The aim in this note is to define an algorithm to carry out minimal curvature spherical harmonics interpolation, which is then used to calculate the Laplacian for multi-electrode EEG data analysis. The approach taken is to respect the data.…
We study the consistency of minimum-norm interpolation in reproducing kernel Hilbert spaces corresponding to bounded kernels. Our main result give lower bounds for the generalization error of the kernel interpolation measured in a…
For solving linear ill-posed problems regularization methods are required when the right hand side is with some noise. In the present paper regularized solutions are obtained by implicit iteration methods in Hilbert scales. % By exploiting…
For a division ring $\mathbb F$, the polynomials $f\in\mathbb F$ can be evaluated "on the left" and "on the right" giving rise to left and right Lagrange interpolation problems. The problems containig interpolation conditions of the same…
Multilinear interpolation is a powerful tool used in obtaining strong type boundedness for a variety of operators assuming only a finite set of restricted weak-type estimates. A typical situation occurs when one knows that a multilinear…
The Hermite-Birkhoff interpolation problem of a function given on arbitrarily distributed points on the sphere and other manifolds is considered. Each proposed interpolant is expressed as a linear combination of basis functions, the…
Consider the Poisson equation with the Dirichlet boundary condition on a three-dimensional polyhedral domain. For singular solutions from the non-smoothness of the domain boundary, we propose new anisotropic tetrahedral mesh refinement…
Despite the impressive precision of the Z-pole measurements made at LEP and SLC, the allowed region for the principle Standard Model parameters responsible for radiative corrections (the mass of the Higgs, the mass of the top and alpha(Mz))…
This work investigates theoretically the interplay between interpolation and aggregation in regression. We establish that the $\gamma$-graph dimension characterizes learnability for a broad class of natural aggregation procedures.…
We give a complete characterization of limiting interpolation spa\-ces for the real method of interpolation using extrapolation theory. For this purpose the usual tools (e.g., Boyd indices or the boundedness of Hardy type operators) are not…
An extension of Marcinkiewicz Interpolation Theorem, allowing intermediate spaces of Orlicz type, is proved. This generalization yields a necessary and sufficient condition so that every quasilinear operator, which maps the set, $S(X,\mu)$,…
This paper constructs unique compactly supported functions in Sobolev spaces that have minimal norm, maximal support, and maximal central value, under certain renormalizations. They may serve as optimized basis functions in interpolation or…