A de Montessus-type theorem for CF approximation
نویسندگان
چکیده
منابع مشابه
A Montessus de Ballore Theorem for M ultivariate Pad6 Approximants
During the last few years several authors have tried to generalize the concept of Pad& approximant to multivariate functions and to prove a generalization of Montessus de Ballore’s theorem. We refer, e.g., to J. Chisholm and P. Graves-Morris (Proc. Roy. Sot. London Ser. A 342 (1975), 341-372), J. Karlsson and H. Wallin (“Pad& and Rational Approximations and Applications” (E. B. Saff and R. S. V...
متن کاملExtension of “A multivariate convergence theorem of the “de Montessus de Ballore” type” to multipoles
The univariate theorem deals with the case of simple poles as well as with the case t multiple poles. The former means that we have information on the denominator of th meromorphic function while the latter means that we also have information on the derivative ef that denominator. Up to now w-e o+ ,...; prtivcd a multivariate analogon of the univariate d Montessus dc Baiiore theorem for the cas...
متن کاملA multivariate convergence theorem of the “de Montessus de Ballore” type
The univariate theorem of “de Montessus de Ballore” proves the convergence of column sequences of Pad6 approximants for functions f(z) meromorphic in a disk, in case the number of poles of f(z) and their multiplicity is known in advance. We prove here a multivariate analogon for the case of “simple” poles and for the general order Pad& approximants as introduced by Cuyt and Verdonk (1984).
متن کاملDe Branges’ Theorem on Approximation Problems of Bernstein Type
The Bernstein approximation problem is to determine whether or not the space of all polynomials is dense in a given weighted C0-space on the real line. A theorem of de Branges characterizes non-density by existence of an entire function of Krein class being related with the weight in a certain way. An analogous result holds true for weighted sup-norm approximation by entire functions of exponen...
متن کاملA de Montessus type convergence study of a least-squares vector-valued rational interpolation procedure
In a recent paper of the author [A. Sidi, A new approach to vector-valued rational interpolation, J. Approx. Theory 130 (2004) 177–187], three new interpolation procedures for vector-valued functions F(z), where F : C → CN , were proposed, and some of their algebraic properties were studied. One of these procedures, denoted IMPE, was defined via the solution of a linear least-squares problem. I...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 1986
ISSN: 0377-0427
DOI: 10.1016/0377-0427(86)90099-3