IJPAM: Volume 74, No. 3 (2012)

SOME REMARKS ON NEWTON'S ALGORITHM - II

Melisa Hendrata$^1$, P.K. Subramanian$^2$
$^{1,2}$Department of Mathematics
California State University
Los Angeles, State University Drive, Los Angeles, CA 90032, USA


Abstract. We consider Newton's algorithm as well as a variant, the Gauss-Newton algorithm, to solve a system of nonlinear equations $F(x)=0$, where $x \in \R^n, \ F:\R^n \to \R^n$. We use a line search method to ensure global convergence. The exact form of our algorithm depends on the rank of the Jacobian $J(x)$ of $F$. Computational results on some standard test problems are presented, which show that the algorithm may be viable.

Received: November 17, 2011

AMS Subject Classification: 90, 90-08

Key Words and Phrases: Newton's method, Armijo line search, Gauss-Newton algorithm, nonlinear equations

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 74
Issue: 3