## Directional Newton Methods in n Variables

### Authors: Yuri Levin and Adi Ben-Israel

ABSTRACT

Directional Newton methods for functions $f$ of $n$ variables are shown to converge, under typical assumptions, to a solution of $f(\mathbf{x})=0$. The rate of convergence is quadratic, for near-gradient directions, and directions along components of the gradient of $f$ with maximal modulus. These methods are applied to solving systems of equations without inversion of the Jacobian matrix.

Key words and phrases. Newton Method, Single equations, Systems of equations

Mathematics Subject Classification. Primary 65H05, 65H10; Secondary 49M15

Paper Available at: ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-13.ps.gz