Nondiagonal quadratic Hermite-Padé approximation to the exponential function

Quadratic Hermite-Padé polynomials associated with the exponential function

Quadratic Hermite-Pad6 Approximation to the Exponential Function

Approximation to exp of the form f~m(z) := pro(z) e -2z + qm(7.) e -Z + rm(z) = O(z3C"+t)-l), where p,., qm, and r,, are polynomials of degree at most m and p,, has lead coefficient 1 is considered. Exact asymptotics and explicit formulas are obtained for the sequences {~gm}, {P,,}, {qm}, and {rm}. It is observed that the above sequences all satisfy the simple four-term recursion: 1 Tin+ 3 = ~ ...

Generalized Hermite-Padé approximation for Nikishin systems of three functions

Nikishin systems of three functions are considered. For such systems, the rate of convergence of simultaneous interpolating rational approximations with partially prescribed poles is studied. The solution is described in terms of the solution of a vector equilibrium problem in the presence of a vector external field.

Scaled and Squared Subdiagonal Padé Approximation for the Matrix Exponential

The scaling and squaring method is the most widely used algorithm for computing the exponential of a square matrix A. We introduce an efficient variant that uses a much smaller squaring factor when ‖A‖ 1 and a subdiagonal Padé approximant of low degree, thereby significantly reducing the overall cost and avoiding the potential instability caused by overscaling, while giving forward error of the...

Analysis of Magneto-hydrodynamics Jeffery-Hamel Flow with Nanoparticles by Hermite-Padé Approximation

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...