Related papers: Geometric Multiproducts: A New Extrapolation Tool
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…
Physically relevant field-theoretic quantities are usually derived from perturbation techniques. These quantities are solved in the form of an asymptotic series in powers of small perturbation parameters related to the physical system, and…
Taylor expansions of analytic functions are considered with respect to several points, allowing confluence of any of them. Cauchy-type formulas are given for coefficients and remainders in the expansions, and the regions of convergence are…
This paper considers application of the SALSA algorithm as a method of forecasting and applies it to simulated electrical signal, temperature recording from the Australian Bureau of Meteorology and stock prices from the Australian stock…
Machine learning systems, especially with overparameterized deep neural networks, can generalize to novel test instances drawn from the same distribution as the training data. However, they fare poorly when evaluated on out-of-support test…
Loop integration results have been obtained using numerical integration and extrapolation. An extrapolation to the limit is performed with respect to a parameter in the integrand which tends to zero. Results are given for a non-scalar…
We present a generic solution to the fundamental problem of how to connect two points in a plane by a smooth curve that goes through these points with a given slope. The smoothness of any curve depends both on its curvature and its length.…
We introduce a class of functions which constitutes an obvious elliptic generalization of multiple polylogarithms. A subset of these functions appears naturally in the \epsilon-expansion of the imaginary part of the two-loop massive sunrise…
Recently, quantum corrections to optical conductivity of disordered metals up to the UV region were observed. Although this increase of conductivity with frequency, also called anti-Drude behaviour, should disappear at the electron…
The Euclidean algorithm makes possible a simple but powerful generalization of Taylor's theorem. Instead of expanding a function in a series around a single point, one spreads out the spectrum to include any number of points with given…
Mean value interpolation is a method for fitting a smooth function to piecewise-linear data prescribed on the boundary of a polygon of arbitrary shape, and has applications in computer graphics and curve and surface modelling. The method…
In this paper, we derive new asymptotic expansions for the solutions of higher order elliptic equations in the presence of small inclusions. As a byproduct, we derive a topological derivative based algorithm for the reconstruction of…
We present a nodal interpolation method to approximate a subdivision model. The main application is to model and represent curved geometry without gaps and preserving the required simulation intent. Accordingly, we devise the technique to…
Expansions of physical functions are controlled by their singularities, which have special structure because they themselves are physical, corresponding to instantons, caustics or saddle configurations. Resurgent asymptotics formalizes this…
The aim of this paper is to extend the approximate quasi-interpolation on a uniform grid by dilated shifts of a smooth and rapidly decaying function on a uniform grid to scattered data quasi-interpolation. It is shown that high order…
Based on tensor neural network, we propose an interpolation method for high dimensional non-tensor-product-type functions. This interpolation scheme is designed by using the tensor neural network based machine learning method. This means…
In the present paper we will introduce a new approach to multivariate interpolation by employing polyharmonic functions as interpolants, i.e. by solutions of higher order elliptic equations. We assume that the data arise from $C^{\infty}$…
Multivariate functions emerge naturally in a wide variety of data-driven models. Popular choices are expressions in the form of basis expansions or neural networks. While highly effective, the resulting functions tend to be hard to…
The problem of extrapolating the series in powers of small variables to the region of large variables is addressed. Such a problem is typical of quantum theory and statistical physics. A method of extrapolation is developed based on…
We show how one can do algebraic geometry with respect to the category of simplicial objects in an exact category. As a biproduct, we get a theory of derived analytic geometry.