In this paper we generalize the notion of orthogonal Laurent polynomials to orthogonal rational functions. Orthogonality is considered with respect to a measure on the positive real line. From this, Gauss-type quadrature formulas are derived and multipoint Padé approximants for the Stieltjes transform of the measure. Convergence of both the quadrature formula and the multipoint Padé approximant...

A standard approach to reduced-order modeling of higher-order linear dynamical systems is to rewrite the system as an equivalent first-order system and then employ Krylov-subspace techniques for reduced-order modeling of first-order systems. While this approach results in reduced-order models that are characterized as Padé-type or even true Padé approximants of the system’s transfer function, i...

A new algorithm is developed for computing arbitrary real powers Ap of a matrix A ∈ Cn×n. The algorithm starts with a Schur decomposition, takes k square roots of the triangular factor T , evaluates an [m/m] Padé approximant of (1 − x)p at I − T 1/2 , and squares the result k times. The parameters k and m are chosen to minimize the cost subject to achieving double precision accuracy in the eval...

The homotopy perturbation method (HPM) is coupled with versions of Laplace-Padé and Padé methods to provide an approximate solution to the nonlinear differential equation that describes the behaviour of a flow with a stretching flat boundary due to partial slip. Comparing results between approximate and numerical solutions, we concluded that our results are capable of providing an accurate solu...

The Padé approximation is a useful method for creating new inequalities and improving certain inequalities. In this paper we use the Padé approximant to give the refinements of some remarkable inequalities involving inverse trigonometric functions, it is shown that the new inequalities presented in this paper are more refined than that obtained in earlier papers.

Neste trabalho, uma solução para o problema da cinética espacial na teoria difusão de nêutrons multigrupo em geometria cartesiana unidimensional é derivada. A partir divisão do domínio nodos homogêneos, integração nodal aplicada nas equações espacial, obtendo variáveis médias cada nodo: fluxos, concentrações precursores e densidades correntes. As correntes interface são aproximadas pela média p...

In this paper we prove a conjecture on a common region of a convergence of Padé iterations for the matrix sector function. For this purpose we show that all Padé approximants to a special case of hypergeometric function have a power series expansion with positive coefficients. Using a sharpened version of Schwarz’s lemma, we also demonstrate a better estimate of the convergence speed. Our resul...

A numerical method for solving the Flierl–Petviashivili (FP) equation and its variants is proposed. The proposed scheme is based on differential transform method (DTM) and Padé approximants. The DTM-Padé technique introduces an alternative framework designed to overcome the difficulty of the singular point at x = 0. The numerical results demonstrates the validity and applicability of the method...