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On approximate zeros and rootfinding algorithms for a complex polynomial

Author: Myong-Hi Kim
Journal: Math. Comp. 51 (1988), 707-719
MSC: Primary 65H05; Secondary 30C15, 65E05
MathSciNet review: 958638
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Abstract: In this paper we give criteria for a complex number to be an approximate zero of a polynomial f for Newton's method or for the kth-order Euler method. An approximate zero for the kth-order Euler method is an initial point from which the method converges with an order $ (k + 1)$ Also, we construct families of Newton (and Euler) type algorithms which are surely convergent.

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Article copyright: © Copyright 1988 American Mathematical Society

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