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Convergence of Multipoint Padé-type Approximants
Authors:B de la Calle Ysern  G Lpez Lagomasino
Institution:Departamento de Matemática Aplicada, E.T.S. de Ingenieros Industriales, Universidad Politécnica de Madrid, José G. Abascal 2, 28006, Madrid, Spainf1;Departamento de Matemáticas, Escuela Politécnica Superior, Universidad Carlos III de Madrid, Universidad 30, 28911, Leganés, Spain, f2
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 C\I and r(∞)=0. We consider multipoint rational interpolants of the function 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 C\I.
Keywords:
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