Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-27T04:39:53.388Z Has data issue: false hasContentIssue false
  • English
  • Français

On the convergence of iterative processes for the solution of simultaneous equations in several variables

Published online by Cambridge University Press:  24 October 2008

W. F. Bodmer
W. F. Bodmer
Affiliation:
Department of GeneticsCambridge University
Get access Rights & Permissions [Opens in a new window]

Extract

The notion of the order of convergence of iterative processes may well have been known to Gauss or even Newton, but to the author's knowledge it was first considered in detail in 1870 by Schröder(5). The subject was later investigated independently by Hartree(4) and Bodewig(1). Hartree alone mentions, briefly, the extension from one to several variables, but gives no detailed analysis. Domb and Fisher(2) consider a particular type of iterative process in several variables, which they call ‘degenerate’, in which all the variables tend to the same value. We shall follow essentially Hartree's treatment, in considering the solution of r simultaneous equations in r variables and applications to a generalization of the Newton-Raphson process.

Type
Research Notes
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 56 , Issue 3 , July 1960 , pp. 286 - 289
Copyright
Copyright © Cambridge Philosophical Society 1960

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.)

References

REFERENCES

(1)Bodewig, E.Quart. Appl. Math. 7 (1949), 325.CrossRefGoogle Scholar
(2)Domb, C. and Fisher, M. E.Proc. Camb. Phil. Soc. 52 (1956), 652.CrossRefGoogle Scholar
(3)Fisher, R. A.Statistical methods and scientific inference (London, 1956).Google Scholar
(4)Hartree, D. R.Proc. Camb. Phil. Soc. 45 (1949), 230.CrossRefGoogle Scholar
(5)Schröder, E.Math. Ann. 2 (1870), 317.CrossRefGoogle Scholar
(6)Whittaker, E. T. and Robinson, G.Calculus of observations (London, 1946).Google Scholar