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 | References | Similar Articles | Additional Information

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 *k*th-order Euler method. An approximate zero for the *k*th-order Euler method is an initial point from which the method converges with an order Also, we construct families of Newton (and Euler) type algorithms which are surely convergent.

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DOI:
https://doi.org/10.1090/S0025-5718-1988-0958638-1

Article copyright:
© Copyright 1988
American Mathematical Society