Expand all Collapse all | Results 1 - 2 of 2 |
1. CJM 2006 (vol 58 pp. 249)
Convergence of Fourier--PadÃ© Approximants for Stieltjes Functions We prove convergence of diagonal multipoint Pad\'e approximants of
Stieltjes-type functions when a certain moment problem is
determinate. This is used for the study of the convergence of
Fourier--Pad\'e and nonlinear Fourier--Pad\'e approximants for such
type of functions.
Keywords:rational approximation, multipoint PadÃ© approximants, Fourier--PadÃ© approximants, moment problem Categories:41A20, 41A21, 44A60 |
2. CJM 1997 (vol 49 pp. 1034)
Ray sequences of best rational approximants for $|x|^\alpha$ The convergence behavior of best uniform rational
approximations $r^\ast_{mn}$ with numerator degree~$m$
and denominator degree~$n$ to the function $|x|^\alpha$,
$\alpha>0$, on $[-1,1]$ is investigated. It is assumed
that the indices $(m,n)$ progress along a ray sequence in
the lower triangle of the Walsh table, {\it i.e.} the
sequence of indices $\{ (m,n)\}$ satisfies
$$
{m\over n}\rightarrow c\in [1, \infty)\quad\hbox{as } m+
n\rightarrow\infty.
$$
In addition to the convergence behavior, the asymptotic
distribution of poles and zeros of the approximants and the
distribution of the extreme points of the error function
$|x|^\alpha - r^\ast_{mn} (x)$ on $[-1,1]$ will be studied.
The results will be compared with those for paradiagonal
sequences $(m=n+2[\alpha/2])$ and for sequences of best
polynomial approximants.
Keywords:Walsh table, rational approximation, best approximation,, distribution of poles and zeros. Categories:41A25, 41A44 |