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Whittaker's method for systems of non-linear equations

Published online by Cambridge University Press:  24 October 2008

R. A. Nicolaides
R. A. Nicolaides
Affiliation:
Woolwich Polytechnic, London, S.E.18†
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Extract

This paper is concerned with a generalization to n dimensions of a method for obtaining an approximation to a root of an algebraic or transcendental equation. We prove a convergence theorem for the method, and show how the method becomes of considerable practical utility in the case when the Jacobian matrix of the functions constituting the system is strictly diagonally dominant in a neighbourhood.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 65 , Issue 2 , March 1969 , pp. 523 - 526
Copyright
Copyright © Cambridge Philosophical Society 1969

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References

REFERENCES

(1)Henrici, P.Discrete variable methods in ordinary differential equations, p. 366 (John Wiley, 1962).Google Scholar
(2)Whittaker, E. and Robinson, G.The calculus of observations, p. 90 (Dover, 1967).Google Scholar
(3)Weissinger, J.Zur theorie und Anwendung des Iterationsverfahrens. Math. Nachr. 8 (1952), 193–212.CrossRefGoogle Scholar