On the worst-case arithmetic complexity of approximating zeros of polynomials (Q1101184)
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scientific article; zbMATH DE number 4046964
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the worst-case arithmetic complexity of approximating zeros of polynomials |
scientific article; zbMATH DE number 4046964 |
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On the worst-case arithmetic complexity of approximating zeros of polynomials (English)
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1987
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For complex polynomials \(P_ d(R)\) of degree \(d\geq 2\) with all zeros \(z_ i\) satisfying \(| z_ i| \leq R\) it is shown that the worst- case computational complexity of obtaining an \(\epsilon\)-approximation for the zeros of \(P_ d(R)\) is O(log log(R/\(\epsilon)\)). Further a new algorithm, based on Newton's method, and using the Schur-Cohn algorithm, giving upper bounds is derived.
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zeros of polynomials
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worst-case computational complexity
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Newton's method
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Schur-Cohn algorithm
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upper bounds
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