We show that solution to the Hermite–Padé type I approximation problem leads in a natural way subclass of solutions Hirota (discrete Kadomtsev–Petviashvili) system and its adjoint linear problem. Our result explains appearance various ingredients integrable systems theory application multiple orthogonal polynomials, numerical algorithms, random matrices, other branches mathematical physics appl...

Diagonal cubic Hermite-Padé approximation to the exponential function with coefficient polynomials of degree at most m is considered. Explicit formulas and differential equations are obtained for the coefficient polynomials. An exact asymptotic expression is obtained for the error function and it is also shown that these generalized Padé-type approximations can be used to asymptotically minimiz...

In this note we consider the stability preserving properties of diagonal Padé approximations to the matrix exponential. We show that while diagonal Padé approximations preserve quadratic stability when going from continuous-time to discrete-time, the converse is not true. We discuss the implications of this result for discretizing switched linear systems. We also show that for continuous-time s...

We rederive AdS/CFT predictions for infrared two-point functions by an entirely four dimensional approach, without reference to holography. This approach, originally due to Migdal in the context of QCD, utilizes an extrapolation from the ultraviolet to the infrared using a Padé approximation of the two-point function. We show that the Padé approximation and AdS/CFT give the same leading order p...

in this paper, an integration of a symbolic power series method - padé approximation technique (ps - padé), was utilized to solve a system of nonlinear differential equations arising from the similarity solution of laminar thermal boundary layer over a flat plate subjected to a convective surface boundary condition. as both boundary conditions tended to infinity, the combination of series solut...

In this paper, the nonlinear differential equation for the convection of the temperature distribution of a straight fin  with the thermal conductivity depends on the temperature is solved using Adomian Decomposition Method and Padé approximation(PADM) for boundary problems. Actual results are then compared with results obtained previously  using digital solution by Runge–Kuttamethod and a diffe...

The inverse Langevin function cannot be represented in an explicit form and requires an approximation by a series, a non-rational or a rational function as for example by a Padé approximation. In the current paper an analytical method based on the Padé technique and the multiple point interpolation is presented for the inverse Langevin function. Thus, a new simple and accurate approximation of ...

While the concept of Padé approximant is essentially several centuries old, its multivariate version dates only from the early seventies. In the last century many univariate convergence results were proven, describing the approximation power for several function classes. It is not our aim to give a general review of the univariate case, but to discuss only these theorems that have a multivariat...