Related papers: An analog of the Sinc approximation for periodic f…
We develop the convergence theory for a well-known method for the interpolation of functions on the real axis with rational functions. Precise new error estimates for the interpolant are de- rived using existing theory for trigonometric…
In metrics of spaces $L_{s}, \ 1\leq s\leq\infty$, we find asymptotic equalities for upper bounds of approximations by Fourier sums on classes of generalized Poisson integrals of periodic functions, which belong to unit ball of space…
We prove analogues for elliptic interpolation functions of Macdonald's version of the Littlewood identity for (skew) Macdonald polynomials, in the process developing an interpretation of general elliptic "hypergeometric" sums as skew…
In this paper, we introduce a new method for calculating fractional integrals and differentials. The method involves an equation that we have obtained from infinite applied integration by parts. The equation works for special class of…
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.
A method for approximating continuous functions $\mathbb{Z}_{p}^{n}\rightarrow\mathbb{Z}_{p}$ by a linear superposition of continuous functions $\mathbb{Z}_{p}\rightarrow\mathbb{Z}_{p}$ is presented and a polynomial regression model is…
Approximation theorem is one of the most important aspects of numerical analysis that has evolved over the years with many different approaches. Some of the most popular approximation methods include the Lebesgue approximation theorem, the…
In this paper we present a finite field analogue for one of the Appell series. We shall derive its transformations, reduction formulas as well as generating functions.
Numerical interpolation techniques are widely employed for calculating large rational functions in scattering amplitude computations. It has been observed in recent years that these rational functions greatly simplify upon partial…
This work is concerned with the kernel-based approximation of a complex-valued function from data, where the frequency response function of a partial differential equation in the frequency domain is of particular interest. In this setting,…
Ohno's relation is a well-known relation on the field of the multiple zeta values and has an interpolation to complex function. In this paper, we call its complex function Ohno function and study it. We consider the region of absolute…
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…
The notion of supershift generalizes that one of superoscillation and expresses the fact that the sampling of a function in an interval allows to compute the values of the function outside the interval. In a previous paper we discussed the…
System identification is an important area of science, which aims to describe the characteristics of the system, representing them by mathematical models. Since many of these models can be seen as recursive functions, it is extremely…
We obtain estimates exact in order for deviations of Zygmund sums in metrics of spaces $L_{q}$, $1<q<\infty$, on classes of $2\pi$-periodic functions, that admit the representation in the form of convolution of functions that belong to unit…
Interpolation and approximation of functionals with conditionally positive definite kernels is considered on sets of centers that are not determining for polynomials. It is shown that polynomial consistency is sufficient in order to define…
Chebychev approximations are given for the Gamma and the Polygamma functions in only one contiguous intervall [1..inf] with a definable maximal relative error. The approximations need about three coefficients per decimal until a checked…
In this paper, we introduce a method of converting implicit equations to the usual forms of functions locally without differentiability. For a system of implicit equations which are equipped with continuous functions, if there are unique…
We test the Sinc function representation, a novel method for numerically evaluating Feynman diagrams, by using it to evaluate the three-loop master diagrams. Analytical results have been obtained for all these diagrams, and we find…
We have shown recently that integration of the error function ${\rm{erf}}\left( x \right)$ represented in form of a sum of the Gaussian functions provides an asymptotic expansion series for the constant pi. In this work we derive a rational…