Initial approximations in Euler-Chebyshev's method (Q1899955)
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scientific article; zbMATH DE number 804739
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Initial approximations in Euler-Chebyshev's method |
scientific article; zbMATH DE number 804739 |
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Initial approximations in Euler-Chebyshev's method (English)
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20 November 1995
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The author considers a polynomial \(f(x)\) of degree \(n\) and the Euler-Chebyshev iterative method for approximating its zeros. He proves that for any monic polynomial \(f(x)\) of degree \(n\), there exists a set \(\Gamma_f\subset \mathbb{C}^n\) such that the Euler-Chebyshev method starting from \(x^0= x\in \Gamma_f\) does not converge to the zeros of \(f(x)\).
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initial approximations
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polynomial zeros
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Euler-Chebyshev iterative method
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