Kronrod's procedure is a method for estimating the error in Gaussian quadrature methods. Padé approximants are formal Gaussian quadrature formulas. In a previous paper, Kronrod's method was used to obtain .estimates of the error in Padé approximation. Using a new interpretation of this procedure and three different expressions of the error of Padé approximants, extensions of the method are obta...

The divergent Rayleigh-Schrr odinger perturbation expansions for energy eigenvalues of cubic, quartic, sextic and octic oscillators are summed using algebraic approximants. These approximants are generalized Pad e approximants that are obtained from an algebraic equation of arbitrary degree. Numerical results indicate that given enough terms in the asymptotic expansion the rate of convergence o...

The order of the post-Newtonian expansion needed to extract in a reliable and accurate manner the fully general relativistic gravitational wave signal from inspiraling compact binaries is explored. A class of approximate wave forms, called P-approximants, is constructed based on the following two inputs: ~a! the introduction of two new energy-type and flux-type functions e(v) and f (v), respect...

This paper proposed a new approach of controller design. By using model matching method we design a PID controller for higher order system. A higher order model is reduced by Pade approximation and mixed method, then design a controller for reduced order model. We take a comparatively study between close loop response of higher order system and reduced order system. The model order reduction an...

The cluster-variation-Pade-approximant method is a recently proposed tool, based on the extrapolation of low- and 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...

The work  addressed in this paper is a comparative study between convergence of the  acceleration techniques, diagonal pad'{e} approximants and shanks transforms, on Homotopy analysis method  and Adomian decomposition method for solving  differential equations of integer and fractional orders.

We study AAK-type meromorphic approximants to functions of the form F (z) = ∫ dλ(t ) z − t +R(z), where R is a rational function and λ is a complex measure with compact regular support included in (−1,1), whose argument has bounded variation on the support. The approximation is understood in Lp -norm of the unit circle, p ≥ 2. We dwell on the fact that the denominators of such approximants sati...

Applicability of the previously introduced method of modified diagonal Baker-Gammel approximants is extended to truncated perturbation series (TPS) of any order in gauge theories. The approximants reproduce the TPS when expanded in power series of the gauge coupling parameter to the order of that TPS. The approximants have the favorable property of being exactly invariant under the change of th...

We obtain a result on convergence of Padé approximants for meromorphic functions of Stieltjes type. Connection of Padé approximants with Stieltjes moment problem plays a key role in the proof.