Weighted rational approximation in the complex plane
نویسندگان
چکیده
منابع مشابه
Incomplete Rational Approximation in the Complex Plane
in certain natural regions in the complex plane where Pc, and q. are polynomials of degree cn and n, respectively. In particular we construct natural maximal regions (as a function of ~ and e) where the collection of such rational functions is dense in the analytical functions. So from this point of view we have rather complete analog theorems to the results concerning incomplete polynomials on...
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Given a pair (G,W ) of an open bounded set G in the complex plane and a weight function W (z) which is analytic and different from zero in G, we consider the problem of the locally uniform approximation of any function f(z), which is analytic in G, by weighted polynomials of the form {Wn(z)Pn(z)}n=0, where deg Pn ≤ n. The main result of this paper is a necessary and sufficient condition for suc...
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Given an open bounded set G in the complex plane and a weight function W (z) which is analytic and di erent from zero in G, we consider the problem of locally uniform rational approximation of any function f(z), which is analytic in G, by particular ray sequences of weighted rational functions of the form Wm+n(z)Rm;n(z), where Rm;n(z) = Pm(z)=Qn(z); with deg Pm m and degQn n: The main result of...
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Let f be holomorphically continuable over the complex plane except for finitely many branch points contained in the unit disk. We prove that best rational approximants to f of degree n, in the L2-sense on the unit circle, have poles that asymptotically distribute according to the equilibrium measure on the compact set outside of which f is single-valued and which has minimal Green capacity in t...
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We consider the problem of weighted rectilinear approximation on the plane and offer both exact algorithms and heuristics with provable performance bounds. Let S = {(pi, wi)} be a set of n points pi in the plane, with associated distance-modifying weights wi > 0. We present algorithms for finding the best fit to S among x-monotone rectilinear polylines R with a given number k < n of horizontal ...
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ژورنال
عنوان ژورنال: Journal de Mathématiques Pures et Appliquées
سال: 1999
ISSN: 0021-7824
DOI: 10.1016/s0021-7824(01)80008-8