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Convergence of the Newton-Raphson Method For Arbitary Polynomials

Published online by Cambridge University Press:  03 November 2016

P. Lancaster
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Extract

Readers may be interested in an elementary exposition of the convergence properties of the sequence of iterates obtained by applying the Newton-Raphson process to an arbitrary polynomial. The coefficients of the polynomial may be real or complex. By restricting attention to polynomials we will give some precise results using the least possible analysis, while proofs for more general functions would necessarily require more high-powered methods. The arguments we will use require only an elementary knowledge of limiting processes.

Type
Research Article
Information
The Mathematical Gazette , Volume 48 , Issue 365 , October 1964 , pp. 291 - 295
Copyright
Copyright © Mathematical Association 1964

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References

1. Schröder, E. Ueber unendlich viele Algorithmen zur Auflösung der GleichungenMath. Ann. 2 (1870) 317–365.Google Scholar
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3. Lancaster, P. A generalised Rayleigh quotient iteration for lambda-matrices Arch. Rat. Mech. Anal. 8 (1961) 309–322.Google Scholar