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On some approximation problems for complex polynomials

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Abstract

We consider weighted complex approximation problems of the form

$$\mathop {\min }\limits_{p:p(a) = 1} \mathop {\min }\limits_{z \in \left[ { - 1,1} \right]} \left| {w(z)p(z)} \right|$$

withp ranging over all polynomials of degree ≤n anda purely imaginary. Recent results by Ruscheweyh and Freund forw(z) = 1 and\(w(z) = \sqrt {z + 1}\) are extended to more general weight functions. Moreover, the solution of a complex Zolotarev type problem is given.

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Authors and Affiliations

  1. Institut für Angewandte Mathematik, Universität Würzburg, D-8700, Würzburg, F.R.G.

    Roland Freund

  2. Computer Science Department, Stanford University, 94305, Stanford, California, USA

    Roland Freund

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  1. Roland Freund
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Communicated by Dieter Gaier.

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Freund, R. On some approximation problems for complex polynomials. Constr. Approx 4, 111–121 (1988). https://doi.org/10.1007/BF02075452

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  • DOI: https://doi.org/10.1007/BF02075452

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