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On rational interpolation of the function \(| x|\). (Russian. English summary) Zbl 0687.41021

Summary: The estimates of approximation functions \(| x|\) at a segment [- 1,1] by interpolation rational functions at the Chebyshev-Markov nodes are obtained. The case of a fixed number of geometrically different poles is studied in detail. With some limitations on the poles the estimates obtained are accurate in order.

MSC:

41A20 Approximation by rational functions
41A05 Interpolation in approximation theory
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