On generalization of Obreshkoff-Ehrlich method for simultaneous extraction of all roots of polynomials over an arbitrary Chebyshev system (Q2704757)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On generalization of Obreshkoff-Ehrlich method for simultaneous extraction of all roots of polynomials over an arbitrary Chebyshev system |
scientific article |
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12 March 2001
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root of polynomial
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Chebyshev system
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Obreshkoff-Ehrlich method
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iteration method
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convergence
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On generalization of Obreshkoff-Ehrlich method for simultaneous extraction of all roots of polynomials over an arbitrary Chebyshev system (English)
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The authors consider a generalized polynomial \( f(x) \) on a Chebyshev system over the interval \( (a,b) \) and propose an iteration formula for simultaneous extraction of the roots of the equation \( f(x) = 0 \). This formula is a generalization of iteration formulas of Ehrlich and Obreshkoff. It is proved that the iteration method proposed in this paper has third order of convergence.
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