Related papers: New representations of Pad\'e and Pad\'e-type appr…
While learning the maximum likelihood value of parameters of an undirected graphical model is hard, modelling the posterior distribution over parameters given data is harder. Yet, undirected models are ubiquitous in computer vision and text…
We construct the quasi-classical approximation of the form factors in finite volume using the separation of variables. The latter is closely related to the Baxter equation.
The form factor of the unitary group U(N) endowed with the Haar measure characterizes the correlations within the spectrum of a typical unitary matrix. It can be decomposed into a sum over pairs of ``periodic orbits'', where by periodic…
In this work, we propose an extensive numerical study on approximating the absolute value function. The methods presented in this paper compute approximants in the form of rational functions and have been proposed relatively recently, e.g.,…
We construct a new scheme of approximation of any multivalued algebraic function $f(z)$ by a sequence $\{r_{n}(z)\}_{n\in \mathbb{N}}$ of rational functions. The latter sequence is generated by a recurrence relation which is completely…
In solving the variational problem, the key is to efficiently find the target function that minimizes or maximizes the specified functional. In this paper, by using the Pade approximant, we suggest a methods for the variational problem. By…
We consider row sequences of vector valued Pad\'{e}-Faber approximants (simultaneous Pad\'{e}-Faber approximants) and prove a Montessus de Ballore type theorem.
Given a system of functions $\textup{\textbf{F}}=(F_1,\ldots,F_d),$ analytic on a neighborhood of some compact subset $E$ of the complex plane with simply connected complement, we define a sequence of vector rational functions with common…
A rational approximation by a ratio of polynomial functions is a flexible alternative to polynomial approximation. In particular, rational functions exhibit accurate estimations to nonsmooth and non- Lipschitz functions, where polynomial…
We present a method for constructing global analytical expressions that approximate a function over its entire range. These approximations not only mirror the original function as accurately as desired, but are purposefully created to…
We describe an extension of the Taylor method for the numerical solution of ODEs that uses Pad\'e approximants to obtain extremely precise numerical results. The accuracy of the results is essentially limited only by the computer time and…
Following T. H. Chan, we consider the problem of approximation of a given rational fraction a/q by sums of several rational fractions a_1/q_1, ..., a_n/q_n with smaller denominators. We show that in the special cases of n=3 and n=4 and…
The aim of this study is to examine some numerical tests of Pade approximation for some typical functions with singularities such as simple pole, essential singularity, brunch cut and natural boundary. As pointed out by Baker, it was shown…
The classical continued fraction is generalized for studying the rational approximation problem on multi-formal Laurent series in this paper, the construction is called m-continued fraction. It is proved that the approximants of an…
We give necessary and sufficient conditions for the convergence with geometric rate of the denominators of linear Pad\'e-orthogonal approximants corresponding to a measure supported on a general compact set in the complex plane. Thereby, we…
We study approximation by arbitrary linear combinations of $n$ translates of a single function of periodic functions. We construct some methods of this approximation for functions in a class induced by the convolution with a given function,…
In this article, for a certain subset $\mathcal{X}$ of the extended set of rational numbers, we introduce the notion of {\it best $\mathcal{X}$-approximations} of a real number. The notion of best $\mathcal{X}$-approximation is analogous to…
Polynomial series approximations are a central theme in approximation theory due to their utility in an abundance of numerical applications. The two types of series, which are featured most prominently, are Taylor series expansions and…
We describe how to solve simultaneous Pad\'e approximations over a power series ring $K[[x]]$ for a field $K$ using $O~(n^{\omega - 1} d)$ operations in $K$, where $d$ is the sought precision and $n$ is the number of power series to…
In this paper, approximate solutions for a class of fractional Lane - Emden type equations based on the series expansion method are presented. Various examples are introduced and discussed. The recurrence relation for the components of the…