Padé and Hermite-Padé Approximation and Orthogonality

Sufficient Conditions for the Convergence of Multipoint Hermite-padé Approximants of Nikishin Systems

We consider simultaneous approximation of Nikishin systems of functions by means of rational vector functions which are constructed interpolating along a prescribed table of points. We give sufficient conditions for the uniform convergence of such approximants with a geometric rate.

United Nations Educational Scientific and Cultural Organization and International Atomic Energy Agency THE ABDUS SALAM INTERNATIONAL CENTRE FOR THERORETICAL PHYSICS HERMITE-PADÉ APPROXIMATION APPROACH TO HYDROMAGNETIC FLOWS IN CONVERGENT-DIVERGENT CHANNELS

The problem of two-dimensional, steady, nonlinear flow of an incompressible conducting viscous fluid in convergent-divergent channels under the influence of an externally applied homogeneous magnetic field is studied using a special type of Hermite-Padé approximation approach. This semi-numerical scheme offers some advantages over solutions obtained by using traditional methods such as finite d...

Strong Asymptotics of Hermite-padé Approximants for Angelesco Systems

In this work type II Hermite-Padé approximants for a vector of Cauchy transforms of smooth Jacobi-type densities are considered. It is assumed that densities are supported on mutually disjoint intervals (an Angelesco system with complex weights). The formulae of strong asymptotics are derived for any ray sequence of multi-indices.

The Pole Condition: a Padé Approximation of the Dirichlet to Neumann Operator

On cubic Padé Approximation to the exponential function and its application in solving diffusion-convection equation

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...