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Chebyshev-Blaschke products

Authors:

Chiu Yin TsangAuthors Info & Claims

Journal of Computational and Applied Mathematics, Volume 277, Issue C

Pages 106 - 114

https://doi.org/10.1016/j.cam.2014.08.028

Published: 15 March 2015 Publication History

Abstract

In this paper, we study a special kind of finite Blaschke products called Chebyshev-Blaschke products f n, which can be defined by the Jacobi cosine function cd ( u, ), where R + i . We will show that Chebyshev-Blaschke products solve a number of approximation problems, which are related to Zolotarev's 3rd and 4th problems. More importantly, such a Chebyshev-Blaschke product f n, will be shown to be the finite Blaschke product of degree n which has the least deviation from zero on - k ( ), k ( ), where k ( ) is the elliptic modulus. Moreover, certain differential equations for Chebyshev-Blaschke products will be derived.

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Cited By

Beckermann BBisch JLuce R(2022)On the rational approximation of Markov functions, with applications to the computation of Markov functions of Toeplitz matricesNumerical Algorithms10.1007/s11075-022-01256-491:1(109-144)Online publication date: 1-Sep-2022
https://dl.acm.org/doi/10.1007/s11075-022-01256-4

Chebyshev-Blaschke products
1. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
2. Theory of computation

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cover image Journal of Computational and Applied Mathematics

Journal of Computational and Applied Mathematics Volume 277, Issue C

March 2015

216 pages

ISSN:0377-0427

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Copyright © Elsevier B.V.

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Elsevier Science Publishers B. V.

Netherlands

Publication History

Published: 15 March 2015

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Cited By

Beckermann BBisch JLuce R(2022)On the rational approximation of Markov functions, with applications to the computation of Markov functions of Toeplitz matricesNumerical Algorithms10.1007/s11075-022-01256-491:1(109-144)Online publication date: 1-Sep-2022
https://dl.acm.org/doi/10.1007/s11075-022-01256-4

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