Hostname: page-component-848d4c4894-xfwgj Total loading time: 0 Render date: 2024-07-06T16:08:46.150Z Has data issue: false hasContentIssue false
  • English
  • Français

Notes on Numerical Analysis I. Polynomial Iteration

Published online by Cambridge University Press:  20 November 2018

Hans Schwerdtfeger
Hans Schwerdtfeger*
Affiliation:
McGill University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let f(x) be a real analytic function of the real variable x and α a simple root of the equation f(x) = 0. It is well known that a function ϕ(x) can be associated with the equation in many different ways such that

  1. (i) α is a root of the equation ϕ(x), i.e. α is a fixed point (invariant point) of the function ϕ(x);

  2. (ii)

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 2 , Issue 2 , 01 May 1959 , pp. 97 - 110
Copyright
Copyright © Canadian Mathematical Society 1959

References

1. Blaskett, D.R. and Schwerdtfeger, H., A formula for the solution of an arbitrary analytic equation, Quarterly of Applied Mathematics, 3, (1945) 266-268.Google Scholar
2. Coppel, W.A., The solution of equations by iteration, Proceedings of the Cambridge Philosphical Society 51 (1955), 41-43.Google Scholar
3. Domb, C., On iterative solutions of algebraic equations, ibidem 45 (1949), 237-240.Google Scholar
4. Dubrovskii, V.M., O metode iteracii, Uspechi matemat. nauk 9 No. 3 (61) (1954), 127-133.Google Scholar
5. Hartree, D.R., Notes on iterative processes, Proceedings of the Cambridge Philosophical Society 45 (1949), 230-236.Google Scholar
6. Householder, A.S., A class of iterative methods for solving equations (Mathematical Association of America, Gainesville, December 1950) Mimeographed, 16 pp.Google Scholar
7. Householder, A.S. Polynomial iterations to roots of algebraic equations, Proceedings of the American Mathematical Society 2 (1951), 718-719.Google Scholar
8. Householder, A.S. Principles of Numerical Analysis, (New York, 1953), in particular p. 129-131.Google Scholar
9. Ostrowski, A., Vorlesungen über Differential? und Integral- rechnung Vol. 2, (Basel, 1951), in particular p. 334-343.Google Scholar
10. Ottaviani, G., Sulla risoluzione di una equazione con il metodo di iterazione, Sritti mat. in onore di F. Sibirani XIX (1957), 195-199.Google Scholar