Related papers: A regular interpolation problem and its applicatio…
The class $Ts(r,f)$ the trigonometric interpolation splines depending on the parameter vectors, selected convergence factors and interpolation factors is considered. The main properties of simple interpolation trigonometric splines are…
In this technical note, we derive a closed-form expression for the affine transformation mapping local image patches between two calibrated views. We show that the transformation is a function of the relative camera pose, the image…
This note comprises a synthesis of certain results in the theory of exact interpolation between Hilbert spaces. In particular, we examine various characterizations of interpolation spaces and their relations to a number of results in…
The goal of this paper is to design compact support basis spline functions that best approximate a given filter (e.g., an ideal Lowpass filter). The optimum function is found by minimizing the least square problem ($\ell$2 norm of the…
We consider functions $f$ of two real variables, given as trigonometric functions over a finite set $F$ of frequencies. This set is assumed to be closed under rotations in the frequency plane of angle $\frac{2k\pi}{M}$ for some integer $M$.…
We consider the problem of obtaining interpolation constraints for function classes, i.e., necessary and sufficient constraints that a set of points, function values and (sub)gradients must satisfy to ensure the existence of a global…
We construct automorphisms of $\C^n$ which map certain discrete sequences one onto another with prescribed finite jet at each point, thus solving a general Mittag-Leffler interpolation problem for automorphisms. Under certain circumstances,…
For finite dimensional CMV matrices the mixed inverse spectral problem of reconstruction the matrix by its submatrix and a part of its spectrum is considered. A general rational interpolation problem which arises in solving the mixed…
The total generalized variation extends the total variation by incorporating higher-order smoothness. Thus, it can also suffer from similar discretization issues related to isotropy. Inspired by the success of novel discretization schemes…
One of the possible variants of the classification of trigonometric interpolation splines is considered, depending on the chosen convergence factors, the distribution of signs of the basis functions and the interpolation factors. The…
Let $f$ be a $r\times m$-matrix of holomorphic functions that is generically surjective. We provide explicit integral representation of holomorphic $\psi$ such that $\phi=f\psi$, provided that $\phi$ is holomorphic and annihilates a certain…
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…
We study the approximation of maps into complex manifolds along with interpolation on certain compact subsets of the plane. Results are also obtained regarding approximation and interpolation of sections of holomorphic submersions.
In the paper, the planar polynomial geometric interpolation of data points is revisited. Simple sufficient geometric conditions that imply the existence of the interpolant are derived in general. They require data points to be convex in a…
A regular realizability (RR) problem is testing nonemptiness of intersection of some fixed language (filter) with given regular language. We study here complexity of RR problems. It appears that for any language L there exists RR problem…
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…
Laplace interpolation is a popular approach in image inpainting using partial differential equations. The classic approach considers the Laplace equation with mixed boundary conditions. Recently a more general formulation has been proposed…
We prove that two fixed univariate functions, namely, an arbitrary continuous non-affine function and a concrete affine function, are sufficient to approximate continuous functions of one variable under the operations of addition and…
We investigate stochastic interpolation, a recently introduced framework for high dimensional sampling which bears many similarities to diffusion modeling. Stochastic interpolation generates a data sample by first randomly initializing a…
In this paper, an open problem in the multidimensional complex analysis is pesented that arises in the investigation of the regularity properties of Fourier integral operators and in the regularity theory for hyperbolic partial differential…