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Iteration Methods for Finding all Zeros of a Polynomial Simultaneously

Oliver Aberth
Mathematics of Computation
Vol. 27, No. 122 (Apr., 1973), pp. 339-344
DOI: 10.2307/2005621
Stable URL: http://www.jstor.org/stable/2005621
Page Count: 6
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Iteration Methods for Finding all Zeros of a Polynomial Simultaneously
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Abstract

Durand and Kerner independently have proposed a quadratically convergent iteration method for finding all zeros of a polynomial simultaneously. Here, a new derivation of their iteration equation is given, and a second, cubically convergent iteration method is proposed. A relatively simple procedure for choosing the initial approximations is described, which is applicable to either method.

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