Optimal rational functions for the generalized Zolotarev problem in the complex plane (Q2706369)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Optimal rational functions for the generalized Zolotarev problem in the complex plane |
scientific article |
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19 March 2001
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complex Chebyshev approximation
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rational function
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Zolotarev problem
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generalized ADI method
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Optimal rational functions for the generalized Zolotarev problem in the complex plane (English)
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It has been recognised that the determination of optimal parameters for the classical alternating direction implicit (ADI) method leads to the Zolotarev probloem. Generalised rational Zolotarev problem concerns rational functions with the numerator and denominator of different degrees [\textit{N. Levenberg} and \textit{L. Reichel}, Numer. Math. 66, No. 2, 215-233 (1993; Zbl 0797.65030)]. The authors present a method to construct optimal rational functions for the generalised Zolotarev problem in the complex plane. Considering line segments on the real axis and parallel to the imaginary axis, numerical tests for the corresponding Zolotarev problem are given. These examples highlight significant improvements over the classical solution.
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