SCHUR–NEVANLINNA SEQUENCES OF RATIONAL FUNCTIONS
نویسندگان
چکیده
منابع مشابه
Rational Krylov sequences and Orthogonal Rational Functions
In this paper we study the relationship between spectral decomposition, orthogonal rational functions and the rational Lanczos algorithm, based on a simple identity for rational Krylov sequences.
متن کاملRay Sequences of Laurent-type Rational Functions
Abstract. This paper is devoted to the study of asymptotic zero distribution of Laurent-type approximants under certain extremality conditions analogous to the condition of Grothmann [1], which can be traced back to Walsh’s theory of exact harmonic majorants [8, 9]. We also prove results on the convergence of ray sequences of Laurent-type approximants to a function analytic on the closure of a ...
متن کاملSchur-Nevanlinna sequences of rational functions
We study certain sequences of rational functions with poles outside the unit circle. Such kind of sequences are recursively constructed based on sequences of complex numbers with norm less than one. In fact, such sequences are closely related to the Schur-Nevanlinna algorithm for Schur functions on the one hand and on the other hand to orthogonal rational functions on the unit circle. We shall ...
متن کاملRates of Best Uniform Rational Approximation of Analytic Functions by Ray Sequences of Rational Functions
In this paper, problems related to the approximation of a holomorphic function f on a compact subset E of the complex plane C by rational functions from the class Rn,m of all rational functions of order (n,m) are considered. Let ρn,m = ρn,m( f ; E) be the distance of f in the uniform metric on E from the class Rn,m . We obtain results characterizing the rate of convergence to zero of the sequen...
متن کاملOn the Degree of Convergence of Sequences of Rational Functions*
The writer has recently studiedf the convergence of certain sequences of rational functions of the complex variable, under the hypothesis that the poles of these functions are prescribed and satisfy certain asymptotic conditions. The rational functions are determined either by interpolation to a given analytic function, or by some extremal property of best approximation to such a function. Degr...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the Edinburgh Mathematical Society
سال: 2007
ISSN: 0013-0915,1464-3839
DOI: 10.1017/s0013091504001063