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The Solution of Algebraic and Transcendental Equations by Iteration

Published online by Cambridge University Press:  03 November 2016

E. H. Bateman
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Abstract

This note gives a general 2nd order solution, with the corresponding 3rd order correction, by means of which a good numerical answer can be obtained from an approximate estimate in one operation, and results of high accuracy by one or two iterations. The method is applied to integral roots of numbers, and to common types of equations.

For the extraction of square roots and cube roots of high accuracy, the general method is developed in the form of series designed to simplify the computation, and one example is given in full with an accuracy of over 30 significant figures.

Type
Research Article
Information
The Mathematical Gazette , Volume 37 , Issue 320 , May 1953 , pp. 96 - 101
Copyright
Copyright © The Mathematical Association 1953

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References

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