Directional Newton methods in variables

Authors:
Yuri Levin and Adi Ben-Israel

Journal:
Math. Comp. **71** (2002), 251-262

MSC (2000):
Primary 65H05, 65H10; Secondary 49M15

Published electronically:
May 17, 2001

MathSciNet review:
1862998

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Abstract | References | Similar Articles | Additional Information

Directional Newton methods for functions of variables are shown to converge, under standard assumptions, to a solution of . The rate of convergence is quadratic, for near-gradient directions, and directions along components of the gradient of with maximal modulus. These methods are applied to solving systems of equations without inversion of the Jacobian matrix.

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Additional Information

**Yuri Levin**

Affiliation:
RUTCOR–Rutgers Center for Operations Research, Rutgers University, 640 Bartholomew Rd, Piscataway, New Jersey 08854-8003

Email:
ylevin@rutcor.rutgers.edu

**Adi Ben-Israel**

Affiliation:
RUTCOR–Rutgers Center for Operations Research, Rutgers University, 640 Bartholomew Rd, Piscataway, New Jersey 08854-8003

Email:
bisrael@rutcor.rutgers.edu

DOI:
https://doi.org/10.1090/S0025-5718-01-01332-1

Keywords:
Newton method,
single equations,
systems of equations

Received by editor(s):
October 27, 1999

Received by editor(s) in revised form:
May 15, 2000

Published electronically:
May 17, 2001

Additional Notes:
The first author was supported by the Center for Discrete Mathematics and Theoretical Computer Science (DIMACS), Rutgers University

Article copyright:
© Copyright 2001
American Mathematical Society