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Complex Zolotarev Polynomials on the Real Interval [−1, 1]

✍ Scribed by C. Detaille; J.P. Thiran

Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
321 KB
Volume
72
Category
Article
ISSN
0021-9045

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✦ Synopsis

We consider complex Zolotarev polynomials of degree (n) on ([-1,1]), i.e., monic polynomials of degree (n) with the second coefficient assigned to a given complex number (\rho), that have minimum Chebyshev norm on ([-1,1]). They can be characterized either by (n) or by (n+1) extremal points. We show that those corresponding to (n) extrema are closely related to real Zolotarev polynomials on ([-1,1]), so that we distinguish between a trigonometric case where an explicit expression is given and the more complicated elliplic case. The classification of the parameters (\rho) that lead to one of the above cases is provided. 1993 Academic Press. Inc.

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