Abstract
Methods of descent for solving polynomial equations were introduced by Henrici (1974). The following recent developments concerning such methods are presented: (i) A proof, due to Martin (1976), of a result concerning the non-existence of continuous descent functions, which was stated without proof by Henrici; (ii) A descent function with global uniform convergence, introduced by M. Kneser (1981) in connection with a constructive proof of the Fundamental Theorem of Algebra, which is shown to be identical with Newton’s method in the neighborhood of simple zeros.
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Bibliography
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© 1983 D. Reidel Publishing Company
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Henrici, P. (1983). Topics in Computational Complex Analysis: I. Methods of Descent for Polynomial Equations. In: Werner, H., Wuytack, L., Ng, E., Bünger, H.J. (eds) Computational Aspects of Complex Analysis. NATO Advanced Study Institutes Series, vol 102. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-7121-9_5
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DOI: https://doi.org/10.1007/978-94-009-7121-9_5
Publisher Name: Springer, Dordrecht
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