New representations of Padé, Padé-type, and partial Padé approximants
نویسندگان
چکیده
منابع مشابه
Convergence of Multipoint Padé-type Approximants
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 f (z) = dµ(x) z − x + r(z), where some poles are fixed and others are left free. We show that if the interpolati...
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In 1976, Chisholm et al. 1 published a paper concerning the location of poles and zeros of Padé approximants of ln 1 − z developed at the complex point ζ : ln 1 − z ln 1 − ζ − ∑∞ n 1 1/n z − ζ/1 − ζ . They claimed that all poles and zeros of diagonal Padé approximants n/n interlace on the cut z ζ t 1 − ζ , t ∈ 1,∞ . Unfortunately, this result is only partially true, for poles. Klarsfeld remarke...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2015
ISSN: 0377-0427
DOI: 10.1016/j.cam.2014.07.007