Hostname: page-component-cb9f654ff-plnhv Total loading time: 0.001 Render date: 2025-08-24T21:31:13.542Z Has data issue: false hasContentIssue false
  • English
  • Français

The Solution of Algebraic and Transcendental Equations by Iteration

Published online by Cambridge University Press:  03 November 2016

E. H. Bateman
Get access Rights & Permissions [Opens in a new window]

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.

Information

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

1. Burnside, W. S. and Panton, A. W., Theory of Equations (Longmans, Green, 8th Edition, 1918).Google Scholar
2. Whittaker, E. T. and Robinson, G., Calculus of Observations (Blackie, 1924).Google Scholar
3. Haldane, J.B.S., “The Extraction of Square Roots”, The Mathematical Gazette, May 1951.Google Scholar
4. Peter, Gray, Tables for the Formation of Logarithms and Antilogarithms to Twenty-four Places (C. and E. Layton, 2nd Edition, 1900).Google Scholar
5. Bateman, E. H., “Elastic Stress Analysis of a Thin Tube”, Ministry of Supply Report A.D.E./T1/50/12, 1950.Google Scholar