scholarly journals A note on rational Chebyshev approximation on the positive real axis

1974 ◽  
Vol 11 (2) ◽  
pp. 201-202 ◽  
Author(s):  
A.R Reddy
Keyword(s):  
Real Axis ◽  
Chebyshev Approximation ◽  
Positive Real Axis ◽  
Positive Real ◽  
Rational Chebyshev ◽  
Rational Chebyshev Approximation

scholarly journals An Extension of the Almost Isolated Singularity of Finite Exponential Order

1964 ◽  
Vol 14 (2) ◽  
pp. 137-141
Author(s):  
R. Wilson
Keyword(s):  
Real Axis ◽  
Taylor Series ◽  
Positive Real Axis ◽  
Isolated Singularity ◽  
Positive Real ◽  
Small Disk ◽  
Exponential Order ◽  
Disk Centre ◽  
Image Position

Let f(z) be represented on its circle of convergence |z| = 1 by the Taylor seriesand suppose that its sole singularity on |z| = 1 is an almost isolated singularity at z = 1. In the neighbourhood of such a singularity f(z) is regular on a sufficiently small disk, centre z = 1, with the outward drawn radius along the positive real axis excised. If also in this neighbourhood |f(z)| e−(1/δ)ρ remains bounded for some finite ρ, where δ is the distance from the excised radius, then the singularity is said to be of finite exponential order.

Dependence of Best Rational Chebyshev Approximations on the Domain

1977 ◽  
Vol 20 (4) ◽  
pp. 451-454 ◽  
Author(s):  
Charles B. Dunham
Keyword(s):  
Sufficient Conditions ◽  
Chebyshev Approximation ◽  
Error Norm ◽  
Rational Chebyshev ◽  
Rational Chebyshev Approximation

Sufficient conditions are given for the error norm and coefficients of best rational Chebyshev approximation on a domain to depend continuously on the domain. Examples of discontinuity are given.

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