Universal Journal of Computational Mathematics(CEASE PUBLICATION) Vol. 1(3), pp. 73 - 77
DOI: 10.13189/ujcmj.2013.010302
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Cycling in Newton's Method

Mikheev Serge E.^*
Faculty of Applied Mathematics & Control Processes, Saint Petersburg State University, 198504, Russia

ABSTRACT

Cycling in Newton’s method for systems of nonlinear equations in multi-dimensional spaces is researched. The functions of the system have most favorable for convergence properties such as convexity or concavity, no singularity of Jacobi’s matrix for the functions and of course existence of the root. It was shown by the counterexample that these properties do not prevent cycling in pure Newton’s method while various relaxations of the method have good convergence.

KEYWORDS
cycling, cycle, convergence, nonlinear equation, iteration

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Mikheev Serge E. , "Cycling in Newton's Method," Universal Journal of Computational Mathematics(CEASE PUBLICATION), Vol. 1, No. 3, pp. 73 - 77, 2013. DOI: 10.13189/ujcmj.2013.010302.

(b). APA Format:
Mikheev Serge E. (2013). Cycling in Newton's Method. Universal Journal of Computational Mathematics(CEASE PUBLICATION), 1(3), 73 - 77. DOI: 10.13189/ujcmj.2013.010302.