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Mathematics of Computation

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Iteration methods for finding all zeros of a polynomial simultaneously

Author: Oliver Aberth
Journal: Math. Comp. 27 (1973), 339-344
MSC: Primary 65H05
MathSciNet review: 0329236
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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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Keywords: Polynomial zeros, iteration algorithm
Article copyright: © Copyright 1973 American Mathematical Society