The learning capability of a network-based computation model named “Algorithmically Transitive Network (ATN)” is extensively studied using symbolic regression problems. To represent a variety of functions uniformly, the ATN’s topological structure is designed in the form of a truncated power series or a Padé approximant. Since the Padé approximation has better convergence properties than the Ta...

Several construction methods for rational approximations to functions of one real variable are described in the present paper; the computational results that characterize the comparative accuracy of these methods are presented; an effect of error autocorrection is considered. This effect occurs in efficient methods of rational approximation (e.g., Padé approximations, linear and nonlinear Padé–...

For computing Padé approximants, we present presumably stable recursive algorithms that follow two adjacent rows of the Padé table and generalize the well-known classical Levinson and Schur recurrences to the case of a nonnormal Padé table. Singular blocks in the table are crossed by look-ahead steps. Ill-conditioned Padé approximants are skipped also. If the size of these lookahead steps is bo...

While the concept of Padé approximant is essentially several centuries old, its multivariate version dates only from the early seventies. In the last century many univariate convergence results were proven, describing the approximation power for several function classes. It is not our aim to give a general review of the univariate case, but to discuss only these theorems that have a multivariat...

The inverse Langevin function cannot be represented in an explicit form and requires an approximation by a series, a non-rational or a rational function as for example by a Padé approximation. In the current paper an analytical method based on the Padé technique and the multiple point interpolation is presented for the inverse Langevin function. Thus, a new simple and accurate approximation of ...

The cluster variation – Padé approximant method is a recently proposed tool, based on the extrapolation of low/high temperature results obtained with the cluster variation method, for the determination of critical parameters in Ising-like models. Here the method is applied to the three-dimensional simple cubic Ising model, and new results, obtained with an 18-site basic cluster, are reported. O...

We present an asymptotic Padé-approximant estimate for the four-loop coefficients within the linear combination of correlators entering the recently calculated decay rate of a CP-odd Higgs boson, with an assumed mass m A = 100 GeV , into two gluons. All but one of these coefficients are shown to be determined for arbitrary m A from the known 3-loop-order rate by renormalization group methods. A...

Production of emphatic consonants by a speaker of Lebanese Arabic was examined using real-time magnetic resonance imaging (rtMRI). Emphatic consonants were found to be articulated with a lowered, more retracted tongue body than their nonempatic counterparts, with the narrowest emphatic constriction observed in the upper pharynx. Both progressive and regressive emphasis spread was observed; spre...

We study recurrence relations and biorthogonality properties for polynomials and rational functions in the problem of the Padé interpolation in the usual scheme and in the scheme with prescribed poles and zeros. The main result is deriving explicit orthogonality and biorthogonality relations for polynomials and rational functions in both schemes. We show that the simplest linear restrictions in...