Ahsrruct: Section 1 describes the univariate situation in the case of non-normal Pade approximants and Cordellier’s extension of the famous five-star identity of Wynn. Section 2 repeats our definition of multivariate Pade approximants and proves a number of theorems that remain valid when going from the univariate to the multivariate case. These theorems and more new results given in Section 3....

We discuss the analytic continuation beyond μ/T ≃ 1 in QCD at nonzero T and μ by use of the Pade’ approximants. The slope of the critical line obtained in this way increases at large μ with respect to the second order Taylor result.In the hot phase Pade’ and Taylor approximants coincide, suggesting a very large, and possibly infinite, radius of convergence of the Taylor series in this thermodyn...

In this study, an accurate analytical solution for Duffing equations with cubic and quintic nonlinearities is obtainedusing theHomotopyAnalysisMethod (HAM) andHomotopy Pade technique. Novel and accurate analytical solutions for the frequency and displacement are derived. Comparison between the obtained results andnumerical solutions shows that only the first order approximation of the Homotopy ...

The nonlinear oscillator problem has extensive applications. In this paper, we examined the modified homotopy perturbation method to obtain the solution of the problem and to reduce the computational efforts. For the accuracy purpose the Laplace transform and Pade approximation have also been used. We construct the deformation equations by two components of the homotopy series, then by means of...

A mixed method by combining a Eigen algorithm and improved pade approximations is proposed for reducing the order of the large-scale dynamic systems. The most dominant Eigen value of both original and reduced order systems remain same in this method. The proposed method guarantees stability of the reduced model if the original high-order system is stable and is comparable in quality with the ot...

In this paper, we propose a new approach to solve the unsteady gas equation. We apply the Modified Laplace decomposition method (MLDM) coupled with Pade ́ approximation to compute a series solution of unsteady flow of gas through a porous medium. The proposed iterative scheme finds the solution without any discretization, linearization or restrictive assumptions. The nonlinear terms can be easil...

In this paper, a new method is presented to derive a reduced order model for a discrete time systems. This method is based on modified pole clustering technique and pade approximations using bilinear transformations, which are conceptually simple and computer oriented. The denominator polynomial of the reduced order model is obtained by using modified pole clustering technique and numerator coe...

The matrix variational Padé approximant and its generalization to elastic wave scattering are discussed. Predictions of the method for the scattering of a longitudinal plane wave are compared with the exact scattering from spherical voids and inclusions. Its predictions are also compared to those of the first and second Born approximations and to the standard matrix Padé approximant based on th...

Computer graphics experiments led to examples where the graphical approximant is ambient isotopic to a spline, but a slight perturbation of the approximant destroys the isotopic equivalence. These serve as cautionary counterexamples for dynamic visualization of molecular simulations. These visual experiments facilitated the creation of a new operation on splines and formal proofs of its converg...

Padé approximant methods are applied to the known terms of the DRED β-function for N = 1 supersymmetric SU(3) Yang-Mills theory. Each of the [N |M ] approximants with N + M ≤ 4, M 6= 0 constructed from this series exhibits a positive pole which precedes any zeros of the approximant, consistent with the same infrared-attractor pole behaviour known to characterize the exact NSVZ β-function. A sim...