Regulated extensions in rational Chebyshev approximation

Generalized Rational Chebyshev Approximation

In this paper, a generalized rational Chebyshev approximation problem is considered. The problem is this: To minimize the maximum absolute value of the "criterion function" of the error. By imposing a rather natural restriction on the criterion function, the problem is solved completely; the existence, the uniqueness and the characterization of the best approximation are clarified and interesti...

Rational Chebyshev Approximation on the Unit Disk

In a recent paper we showed that er ror curves in po lynomia l Chebyshev a p p r o x i m a t i o n of ana ly t ic functions on the unit disk tend to a p p r o x i m a t e perfect circles abou t the origin [23]. M a k i n g use of a theorem of Ca ra th6odo ry and Fej6r, we der ived in the process a me thod for calculat ing near-bes t a p p r o x i m a t i o n s rapid ly by finding the pr incipal...

CHEBYSHEV RATIONAL APPROXIMATION TO ENTIRE FUNCTIONS IN [ 0 , oc ]

Introduction : Quite recently Chebyshev rational approximation to certain entire functions on the whole positive axis has attracted the attention of many mathematicians. In this respect the papers ([3-7, 9]) are worth mentioning. All these papers have been devoted only to entire functions of finite order. On the other hand, methods developed and used in these papers are valid only to entire fun...

On Convergence and Degeneracy in Rational Padi and Chebyshev Approximation *

We study two questions associated with rational approximation of a function f(z) near the origin z-0: continuity of the Pad approximation operator, and convergence of Chebyshev to Pad ap-proximants as the domain of approximation shrinks to a point. Both become delicate in the case of degenerate approximations, i.e. approximations whose numerator and denominator are deficient in degree. In this ...

Real vs Complex Rational Chebyshev Approximation on an Interval