Related papers: On bivariate fractal approximation
By analogy with the program of McKinnon-Roth, we define and study approximation constants for points of a projective variety X defined over K the function field of an irreducible and non-singular in codimension 1 projective variety defined…
This paper examines functional equivariance, recently introduced by McLachlan and Stern [Found. Comput. Math. (2022)], from the perspective of backward error analysis. We characterize the evolution of certain classes of observables…
This brief survey deals with multi-dimensional Diophantine approximations in sense of linear form and with simultaneous Diophantine approximations. We discuss the phenomenon of degenerate dimension of linear subspaces generated by the best…
Given a multi-valued function $\Phi$ on a topological space $X$ we study the properties of its fixed fractal, which is defined as the closure of the orbit $\Phi^\omega(Fix(\Phi))=\bigcup_{n\in\omega}\Phi^n(Fix(\Phi))$ of the set…
Fractional dissipation is a powerful tool to study non-local physical phenomena such as damping models. The design of geometric, in particular, variational integrators for the numerical simulation of such systems relies on a variational…
In this article, we investigate the fractal dimension of the graph of the mixed Riemann-Liouville fractional integral for various choice of continuous functions on a rectangular region. We estimate bounds for the box dimension and the…
Extension problems for polynomial valuations on different cones of convex functions are investigated. It is shown that for the classes of functions under consideration, the extension problem reduces to a simple geometric obstruction on the…
This work proposes a novel technique for the numerical calculus of the fractal dimension of fractal objects which can be represented as a closed contour. The proposed method maps the fractal contour onto a complex signal and calculates its…
This article presents a reformulation of the Theory of Functional Connections: a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The reformulation presented in this paper exploits…
The fractional calculus is useful to model non-local phenomena. We construct a method to evaluate the fractional Caputo derivative by means of a simple explicit quadratic segmentary interpolation. This method yields to numerical resolution…
In this paper, we introduce a method known as polynomial frame approximation for approximating smooth, multivariate functions defined on irregular domains in $d$ dimensions, where $d$ can be arbitrary. This method is simple, and relies only…
The article is devoted to approximate, global and along curves differentiability of functions over non-archimedean infinite fields with non-trivial valuations. Fields with zero and non-zero characteristics are considered. Spaces of…
Provided a special function of one variable and some of its derivatives can be accurately computed over a finite range, a method is presented to build a series of polynomial approximations of the function with a defined relative error over…
The purpose of this paper is to study the fractal phenomena in large data sets and the associated questions of dimension reduction. We examine situations where the classical Principal Component Analysis is not effective in identifying the…
In this paper we have defined one function that has been used to construct different fractals having fractal dimensions between 1.58 and 2. Also, we tried to calculate the amount of increment of fractal dimension in accordance with the base…
This study reexamines diffusive representations for fractional integrals with the goal of pioneering new variants of such representations. These variants aim to offer highly efficient numerical algorithms for the approximate computation of…
The interpolation-regression approximation is a powerful tool in numerical analysis for reconstructing functions defined on square or triangular domains from their evaluations at a regular set of nodes. The importance of this technique lies…
We study Whitney-type estimates for approximation of convex functions in the uniform norm on various convex multivariate domains while paying a particular attention to the dependence of the involved constants on the dimension and the…
We have developed a method for constructing spectral approximations for convolution operators of Fredholm type. The algorithm we propose is numerically stable and takes advantage of the recurrence relations satisfied by the entries of such…
We exploit dynamical properties of diagonal actions to derive results in Diophantine approximations. In particular, we prove that the continued fraction expansion of almost any point on the middle third Cantor set (with respect to the…