Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 

 

Iteration methods for finding all zeros of a polynomial simultaneously


Author: Oliver Aberth
Journal: Math. Comp. 27 (1973), 339-344
MSC: Primary 65H05
DOI: https://doi.org/10.1090/S0025-5718-1973-0329236-7
MathSciNet review: 0329236
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65H05

Retrieve articles in all journals with MSC: 65H05


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1973-0329236-7
Keywords: Polynomial zeros, iteration algorithm
Article copyright: © Copyright 1973 American Mathematical Society