Related papers: Guerra's interpolation using Derrida-Ruelle cascad…
Let X be a countably infinite set of real numbers and let Y_x, x \in X, be an independent family of stationary random subsets of the real numbers, e.g. homogeneous Poisson point processes. We give criteria for the a.s. existence of various…
This paper contains a review of available methods for establishing improved interpolation inequalities on the sphere for subcritical exponents. Pushing further these techniques we also establish some new results, clarify the range of…
This paper introduces the fractal interpolation problem defined over domains with a nonlinear partition. This setting generalizes known methodologies regarding fractal functions and provides a new holistic approach to fractal interpolation.…
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 problem of the optimal approximation of circular arcs by parametric polynomial curves is considered. The optimality relates to the curvature error. Parametric polynomial curves of low degree are used and a geometric continuity is…
We use Newton divided differences for calculation of Greene sums -- the rational functions determined by linear extensions of partially ordered sets. Identities for Greene sums generate relations for Newton divided differences and Arnold…
In his article "Powerlist: A Structure for Parallel Recursion" Jayadev Misra wrote: "Many data parallel algorithms - Fast Fourier Transform, Batcher's sorting schemes and prefix sum - exhibit recursive structure. We propose a data…
A class of numerical methods to determine Pollicott-Ruelle resonances in chaotic dynamical systems is proposed. This is achieved by relating some existing procedures which make use of Pade approximants and interpolating exponentials to both…
We use a diffuse interface method for solving Poisson's equation with a Dirichlet condition on an embedded curved interface. The resulting diffuse interface problem is identified as a standard Dirichlet problem on approximating regular…
We obtain estimates of the $L_p$-error of the bivariate polynomial interpolation on the Lissajous-Chebyshev node points for wide classes of functions including non-smooth functions of bounded variation in the sense of Hardy-Krause. The…
This paper introduces an interpolation-based method, called the reconstruction approach, for nonparametric regression. Based on the fact that interpolation usually has negligible errors compared to statistical estimation, the reconstruction…
A new hierarchy of operads over the linear spans of $\delta$-cliffs, which are some words of integers, is introduced. These operads are intended to be analogues of the operad of permutations, also known as the associative symmetric operad.…
We explain the origin of the difficulties that appear in a straightforward application of the QRPA in C(12), and we demonstrate that it is imperative to use the projected QRPA (PQRPA). Satisfactory results, not only for the weak processes…
To approximate solutions of a linear differential equation, we project, via trigonometric interpolation, its solution space onto a finite-dimensional space of trigonometric polynomials and construct a matrix representation of the…
Using a residuum approach, we provide a complete description of the space of the rational spatial curves of given tangent directions. The rational Pythagorean hodograph curves are obtained as a special case when the norm of the direction…
Exploiting the deep generative model's remarkable ability of learning the data-manifold structure, some recent researches proposed a geometric data interpolation method based on the geodesic curves on the learned data-manifold. However,…
Delayed processes are ubiquitous throughout biology. These delays may arise through maturation processes or as the result of complex multi-step networks, and mathematical models with distributed delays are increasingly used to capture the…
In the era of big data, we first need to manage the data, which requires us to find missing data or predict the trend, so we need operations including interpolation and data fitting. Interpolation is a process to discover deducing new data…
Veronese webs appear as the natural way of passing to the quotient of curves in the projective space. In thi paper, we give the link between classical multidimensionnal webs and veronse webs by mean of interpolation.
The Hermite interpolation formulas are based on the interpretation of interpolation nodes as roots of suitable polynomials. Therefore, such formulas belong to the class of algebraic interpolations. The article considers a multidimensional…