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Directional Newton methods in  variables
Author(s):
Yuri
Levin;
Adi
Ben-Israel.
Journal:
Math. Comp.
71
(2002),
251-262.
MSC (2000):
Primary 65H05, 65H10;
Secondary 49M15
Posted:
May 17, 2001
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Abstract:
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:
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 and, in revised form May 15, 2000.
Posted:
May 17, 2001
Additional Notes:
The first author was supported by the Center for Discrete Mathematics and Theoretical Computer Science (DIMACS), Rutgers University
Copyright of article:
Copyright
2001,
American Mathematical Society
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