Based on a “monotonicity” analogue of the l’Hospital Rule, monotonicity properties of the relative error are established for a Padé approximation of Mills’ ratio.

We describe some applications of the Euclidean algorithm in modern computational problems like Padé approximation, iterative solution of linear systems, eigenvalue problems, orthogonal polynomials, coding theory etc.

It is well known that the bilinear transform, or first order diagonal Padé approximation to the matrix exponential, preserves quadratic Lyapunov functions between continuous-time and corresponding discrete-time linear time invariant (LTI) systems, regardless of the sampling time. The analagous result also holds for switched linear systems. In this note we show that, for any sampling time, diago...

We present a fraction-free approach to the computation of matrix Padé systems. The method relies on determining a modified Schur complement for the coefficient matrices of the linear systems of equations that are associated to matrix Padé approximation problems. By using this modified Schur complement for these matrices we are able to obtain a fast hybrid fraction-free algorithm for their compu...

The aim of this paper is to introduce a new approximate method, namely the Modified Laplace Padé Decomposition Method (MLPDM) which is a combination of modified Laplace decomposition and Padé approximation to provide an analytical approximate solution to Thomas-Fermi equation. This new iteration approach provides us with a convenient way to approximate solution. A good agreement between the obt...

The combined effects of nanoparticle and magnetic field on the nonlinear Jeffery-Hamel flow are analyzed in the present study. The basic governing equations are solved analytically to nonlinear ordinary differential equation using perturbation method together with a semi-numerical analytical technique called Hermite- Padé approximation. The obtained results are well agreed with that of the Adom...

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...

A method is suggested for interpolating between small-variable and large-variable asymptotic expansions. The method is based on self-similar approximation theory resulting in self-similar root approximants. The latter are more general than the twosided Padé approximants and modified Padé approximants, including these as particular cases. Being more general, the self-similar root approximants gu...

For signal processing, the Wavelet transform (WT) has been shown to be a very promising mathematical tool. WT is efficient for local analysis of nonstationary and fast transient signals due its good estimation of time and frequency localization. In the complex wavelet transform analysis, the modulus maxima and the ± π/2 phase crossings point out the locations of sharp signal transitions. The ph...

It is shown how to find general multivariate Padé approximation using the Gröbner basis technique. This method is more flexible than previous approaches, and several examples are given to illustrate this advantage. When the number of variables is small compared to the degree of approximation, the Gröbner basis technique is more efficient than the linear algebra methods in the literature.