RT Journal Article
T1 Convergence of multipoint Padé-type approximants
A1 Calle Ysern, Bernardo de la
A1 López Lagomasino, Guillermo
AB Let μ be a finite positive Borel measure whose support is a compact subset K of the real line and let I be the convex hull of K. Let r denote a rational function with real coefficients whose poles lie in $\bbfC\setminus I\$ and $r(\infty)=0$. We consider multipoint rational interpolants of the function $$ f(z)=\int {d\mu(x)\over z-x}+r(z) $$, where some poles are fixed and others are left free. We show that if the interpolation points and the fixed poles are chosen conveniently then the sequence of multipoint rational approximants converges geometrically to f in the chordal metric on compact subsets of $\bbfC\setminus I\$.
PB Elsevier
SN 0021-9045
YR 2001
FD 2001-04
LK https://hdl.handle.net/10016/6337
UL https://hdl.handle.net/10016/6337
LA eng
NO 22 pages, no figures.-- MSC2000 code: 41A21.
NO MR#: MR1820896 (2002a:41014)
NO Zbl#: Zbl 0982.41008
NO The second author (G.L.L.) was supported by Dirección General de Enseñanza Superior under Grant PB 96-0120-C03-01 and by INTAS under Grant 93-0219 EXT.
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RD 24 jun. 2024