Related papers: A note on the problem of straight-line interpolati…
The methods of approximation, regularization and smoothing of trigonometric interpolation splines are considered in the paper. It is shown that trigonometric splines can be considered from two points of view - as a trigonometric Fourier…
We prove a finiteness principle for interpolation of data by nonnegative Cm functions. Our result raises the hope that one can start to understand constrained interpolation problems in which e.g. the interpolating function F is required to…
In this work, we study the Hermite interpolation on $n$-dimensional non-equally spaced, rectilinear grids over a field $\Bbbk $ of characteristic zero, given the values of the function at each point of the grid and the partial derivatives…
We study in this paper the function approximation error of multivariate linear extrapolation. The sharp error bound of linear interpolation already exists in the literature. However, linear extrapolation is used far more often in…
We extend the classical theory of variational interpolating splines to the case of compact Riemannian manifolds. Our consideration includes in particular such problems as interpolation of a function by its values on a discrete set of points…
A fast non-polynomial interpolation is proposed in this paper for functions with logarithmic singularities. It can be executed fast with the discrete cosine transform. Based on this interpolation, a new quadrature is proposed for a kind of…
In this paper we study nonlinear interpolation problems for interpolation and peak-interpolation sets of function algebras. The subject goes back to the classical Rudin-Carleson interpolation theorem. In particular, we prove the following…
Matrices resulting from the discretization of a kernel function, e.g., in the context of integral equations or sampling probability distributions, can frequently be approximated by interpolation. In order to improve the efficiency, a…
We prove a complex formulation of the real interpolation method, showing that the real and complex interpolation methods are not inherently real or complex. Using this complex formulation, we prove Stein interpolation for the real…
A lemma of Micchelli's, concerning radial polynomials and weighted sums of point evaluations, is shown to hold for arbitrary linear functionals, as is Schaback's more recent extension of this lemma and Schaback's result concerning…
Deep learning based methods have penetrated many image processing problems and become dominant solutions to these problems. A natural question raised here is "Is there any space for conventional methods on these problems?" In this paper,…
The generic chaining method provides a sharp description of the suprema of many random processes in terms of the geometry of their index sets. The chaining functionals that arise in this theory are however notoriously difficult to control…
The simplest way to obtain continuous interpolation between two points in high dimensional space is to draw a line between them. While previous works focused on the general connectivity between model parameters, we explored linear…
The functional interpolation problem on a continual set of nodes by an integral continued C-fraction is studied. The necessary and sufficient conditions for its solvability are found. As a particular case, the considered integral continued…
In this paper we consider the approximation of a function by its interpolating multilinear spline and the approximation of its derivatives by the derivatives of the corresponding spline. We derive formulas for the uniform approximation…
We consider approximations formed by the sum of a linear combination of given functions enhanced by ridge functions -- a Linear/Ridge expansion. For an explicitly or implicitly given function, we reformulate finding a best Linear/Ridge…
A systematic construction of higher order splines using two hierarchies of polynomials is presented. Explicit instructions on how to implement one of these hierarchies are given. The results are limited to interpolations on regular,…
We formulate a simple algorithm for computing global exact symmetries of closed discrete curves in plane. The method is based on a suitable trigonometric interpolation of vertices of the given polyline and consequent computation of the…
The paper deals with two fundamental types of trigonometric polynomials and splines on uniform grids, which allow us to construct interpolation approximations that depend linearly on the values of the interpolated function. Fundamental on…
The interpolation problem is a natural and fundamental question whose roots trace back to ancient Greece. The story is long and rich, with many chapters, and a complete solution has been obtained only recently. Exploring it leads us on a…