Directional Newton methods in n variables

Authors:
Yuri Levin;Adi Ben-Israel
Affiliations:
RUTCOR-Rutgers Center for Operations Research, Rutgers University, 640 Bartholomew rd, Piscataway, New Jersey;RUTCOR-Rutgers Center for Operations Research, Rutgers University, 640 Bartholomew rd, Piscataway, New Jersey
Venue:
Mathematics of Computation
Year:
2002

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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(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 reversion of the Jacobian matrix.