Explicit formulas for general order multivariate Padé approximants of pseudo-multivariate functions are constructed on specific index sets. Examples include the multivariate forms of the exponential function E (x) = ∞ ∑ j1,j2,...,jm=0 x1 1 x j2 2 · · ·x jm m (j1 + j2 + · · ·+ jm)! , the logarithm function L(x) = ∑ j1+j2+···+jm≥1 x1 1 x j2 2 · · ·x jm m j1 + j2 + · · ·+ jm , the Lauricella funct...

Teresa Yonte and Luis L. Sánchez-Soto Departamento de Óptica, Facultad de F́ısica, Universidad Complutense, 28040 Madrid, Spain (Dated: January 4, 2014) Abstract We characterize the reflectance peak near the Brewster angle for both an interface between two dielectric media and a single slab. To approach this problem analytically, we approximate the reflectance by a first-order diagonal Padé. In ...

Recently the authors have presented the d-transformation which has proved to be very efficient in accelerating the convergence of a large class of infinite series. In this work the d-transformation is modified in a way that suits power series. An economical method for computing the rational approximations arising from the modified transformation is developed. Some properties of these approximan...

Let σ̂ be a Cauchy transform of a possibly complex-valued Borel measure σ and {pn} be a system of orthonormal polynomials with respect to a measure μ, supp(μ)∩ supp(σ) = ∅. An (m,n)-th Frobenius-Padé approximant to σ̂ is a rational function P/Q, deg(P) 6m, deg(Q) 6 n, such that the first m+n+ 1 Fourier coefficients of the linear form Qσ̂−P vanish when the form is developed into a series with respe...

Let be a closed oriented contour on the Riemann sphere. Let E and F be polynomials of degree n + 1, with zeros respectively on the positive and negative sides of . We compute the [n=n] and [n 1=n] Padé denominator at 1 to f (z) = Z 1 z t dt E (t)F (t) : As a consequence, we compute the nth orthogonal polynomial for the weight 1= (EF ). In particular, when is the unit circle, this leads to an ex...

The numerical solution of time-dependent ordinary and partial differential equations presents a number of well known difficulties—including, possibly, severe restrictions on time-step sizes for stability in explicit procedures, as well as need for solution of challenging, generally nonlinear systems of equations in implicit schemes. In this note we introduce a novel class of explicit methods ba...

In this paper, theAdomiandecompositionmethod and Padé approximants are integrated to study thedeflection andpull-in instability of nanocantilever electromechanical switches. In a distributed parameter model, intermolecular forces, including Casimir forces, are taken into account considering their range of application. A closed form power series solution based on Adomian polynomials is obtained....

The Holomorphic Embedding Load-Flow Method (HELM) was recently introduced as a novel technique to constructively solve the power-flow equations in power grids, based on advanced complex analysis. In this paper, the theoretical foundations of the method are established in detail. Starting from a fundamental projective invariance of the power-flow equations, it is shown how to devise holomorphici...

In this paper we review fourth-order approximations of the biharmonic operator in one, two and three dimensions. In addition, we describe recent developments on second and fourth order finite difference approximations of the two dimensional Navier-Stokes equations. The schemes are compact both for the biharmonic and the Laplacian operators. For the convective term the fourth order scheme invoke...

For matrix power series with coefficients over a field, the notion of a matrix power series remainder sequence and its corresponding cofactor sequence are introduced and developed. An algorithm for constructing these sequences is presented. It is shown that the cofactor sequence yields directly a sequence of Pad6 fractions for a matrix power series represented as a quotient B(z)-lA(z). When B(z...