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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.
References:
-
- 1.
- A. Ben-Israel, A Newton-Raphon method for the solution of sytems of equations, J. Math. Anal. Appl. 15(1966), 243-252. MR 34:5273
- 2.
- A. Ben-Israel, Newton's method with modified functions, Contemp. Math. 204(1997), 39-50. MR 98c:65080
- 3.
- I.S. Berezin and N.P. Zhidkov, Computing Methods, Pergamon Press, 1965. MR 30:4372
- 4.
- W. Fleming, Functions of Several Variables, 2nd Edition, Springer, 1977. MR 54:10514
- 5.
- C.-E. Fröberg, Numerical Mathematics: Theory and Computer Applications, Benjamin, 1985. MR 86h:65001
- 6.
- Y. Levin and A. Ben-Israel, MAPLE programs for directional Newton methods are available at: ftp://rutcor.rutgers.edu/pub/bisrael/Newton-Dir.mws.
- 7.
- G. Lukács, The generalized inverse matrix and the surface-surface intersection problem, pp. 167-185 in Theory and Practice of Geometric Modeling (W. Strasser and H.-P. Seidel, editors), Springer-Verlag, 1989. MR 91f:65041
- 8.
- A.M. Ostrowski, Solution of Equations in Euclidean and Banach Spaces, 3rd Edition, Academic Press, 1973. MR 50:11760
- 9.
- A. Ralston and P. Rabinowitz, A First Course in Numerical Analysis, 2nd edition, McGraw-Hill, 1978. MR 58:13599
- 10.
- J. Stoer and K. Bulirsch, Introduction to Numerical Analysis, Springer-Verlag, 1976. MR 83d:65002
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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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