On some approximation problems for complex polynomials |
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Authors: | Roland Freund |
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Institution: | 1. Institut für Angewandte Mathematik, Universit?t Würzburg, D-8700, Würzburg, F.R.G. 2. Computer Science Department, Stanford University, 94305, Stanford, California, USA
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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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