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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Directional Newton methods in $n$ 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:

Directional Newton methods for functions $f$ of $n$ variables are shown to converge, under standard 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.


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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: http://dx.doi.org/10.1090/S0025-5718-01-01332-1
PII: S 0025-5718(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