On the convergence of iterative processes for the solution of simultaneous equations in several variables
Published online by Cambridge University Press: 24 October 2008
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
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