Related papers: Interpolation of Set-Valued Functions
A finite sum of exponential functions may be expressed by a linear combination of powers of the independent variable and by successive integrals of the sum. This is proved for the general case and the connection between the parameters in…
In order to solve an initial value problem by the variational iteration method, a sequence of functions is produced which converges to the solution under some suitable conditions. In the nonlinear case, after a few iterations the terms of…
An algebraic approach is presented for the valuative interpolation problem, which recovers and generalizes prior characterizations known in the complex analytic setting by the authors. We use the asymptotic Samuel function to give the…
Motivated by polynomial approximations of differential forms, we study analytical and numerical properties of a polynomial interpolation problem that relies on function averages over interval segments. The usage of segment data gives rise…
The goal of this note is to show that continuous functions may be approximated using scattered translates of the Poisson kernel.
In environmental applications of extreme value statistics, the underlying stochastic process is often modeled either as a max-stable process in continuous time/space or as a process in the domain of attraction of such a max-stable process.…
This paper introduces the concept of hyperpolation: a way of generalising from a limited set of data points that is a peer to the more familiar concepts of interpolation and extrapolation. Hyperpolation is the task of estimating the value…
Let us assume that $f$ is a continuous function defined on the unit ball of $\mathbb R^d$, of the form $f(x) = g (A x)$, where $A$ is a $k \times d$ matrix and $g$ is a function of $k$ variables for $k \ll d$. We are given a budget $m \in…
We consider non-linear generalizations of fractal interpolating functions applied to functions of one and two variables. The use of such interpolating functions in resizing images is illustrated.
Accurate approximation of a real-valued function depends on two aspects of the available data: the density of inputs within the domain of interest and the variation of the outputs over that domain. There are few methods for assessing…
A numerical procedure and its MAPLE implementation capable of rigorously, albeit in a brute-force manner, proving specific strict one-variable inequalities in specific finite intervals is described. The procedure is useful, for instance, to…
A number of applications require the computation of the trace of a matrix that is implicitly available through a function. A common example of a function is the inverse of a large, sparse matrix, which is the focus of this paper. When the…
The aim of this paper is to characterize a fractal operator associated with multivariate fractal interpolation functions (FIFs) and study the several properties of this fractal operator. Further, with the help of this operator, we…
We obtain sampling and interpolation theorems in radial weighted spaces of analytic functions for weights of arbitrary (more rapid than polynomial) growth. We give an application to invariant subspaces of arbitrary index in large weighted…
Given a continuous function $f:[a,b]\to\mathbb{R}$ such that $f(a)=f(b)$, we investigate the set of distances $|x-y|$ where $f(x)=f(y)$. In particular, we show that the only distances this set must contain are ones which evenly divide…
Soft extrapolation refers to the problem of recovering a function from its samples, multiplied by a fast-decaying window and perturbed by an additive noise, over an interval which is potentially larger than the essential support of the…
This research is concerned with finding the roots of a function in an interval using Chebyshev Interpolation. Numerical results of Chebyshev Interpolation are presented to show that this is a powerful way to simultaneously calculate all the…
Topological entropy is a widely studied indicator of chaos in topological dynamics. Here we give a generalized definition of topological entropy which may be applied to set-valued functions. We demonstrate that some of the well-known…
The work is devoted to the construction of a new interval arithmetic which would combine algorithmic efficiency and high quality estimation of the ranges of expressions.
We consider certain finite sets of circle-valued functions defined on intervals of real numbers and estimate how large the intervals must be for the values of these functions to be uniformly distributed in an approximate way. This is used…