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Convergence of multipoint Padé-type approximants

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URI: https://hdl.handle.net/10016/6337
ISSN: 0021-9045
DOI: 10.1006/jath.2000.3537
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convergence_lagomasino_jat_2001_ps.pdf (221.3 KB)
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2001-04
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Elsevier
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Abstract
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\$.
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22 pages, no figures.-- MSC2000 code: 41A21.
MR#: MR1820896 (2002a:41014)
Zbl#: Zbl 0982.41008
Keywords
Padé-type approximation, Rational approximation, Multi-point approximation, Interpolation, Geometric convergence, Chordal metric, Capacity, Pre-assigned poles
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Journal of Approximation Theory, 2001, vol. 109, n. 2, p. 257-278
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