## DIMACS TR: 2000-13

## 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

DIMACS Home Page