on padé approximation of some practical functions

On Padé Approximation of Some Practical Functions

Analysis of Probabilistic Systems via Generating Functions and Padé Approximation

We investigate the use of generating functions in the analysis of discrete Markov chains. Generating functions are introduced as power series whose coefficients are certain hitting probabilities. Being able to compute such functions implies that the calculation of a number of quantities of interest, including absorption probabilities, expected hitting time and number of visits, and variances th...

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.

Some Remarks on Approximation of Plurisubharmonic Functions

Let Ω be a domain in Cn. An upper semicontinuous function u : Ω → [−∞,∞) is said to be plurisubharmonic if the restriction of u to each complex line is subharmonic (we allow the function identically −∞ to be plurisubharmonic). We say that u is strictly plurisubharmonic if for every z0 ∈ Ω there is a neigbourhood U of z0 and λ > 0 such that u(z) − λ|z|2 is plurisubharmonic on U . We write PSH(Ω)...

Robust Padé Approximation via SVD

Padé approximation is considered from the point of view of robust methods of numerical linear algebra, in particular the singular value decomposition. This leads to an algorithm for practical computation that bypasses most problems of solution of nearly-singular systems and spurious pole-zero pairs caused by rounding errors; a Matlab code is provided. The success of this algorithm suggests that...

Some remarks on Fitzpatrick and Flynn's Gröbner basis technique for Padé approximation

In Fitzpatrick and Flynn (J. Symbolic Comput. 13 (1992) 133), a Gröbner basis technique for multivariable Padé approximation problems was developed under a rather restrictive hypothesis on the shape of the numerator and denominator in relation to the approximation conditions desired. In this article, we show that their hypotheses can be replaced by other less stringent conditions, and we show h...