Generalized Continuation Newton Methods and the Trust-Region Updating Strategy for the Underdetermined System

This paper considers the generalized continuation Newton method and trust-region updating strategy for underdetermined system of nonlinear equations. Moreover, in order to improve its computational efficiency, new will not update Jacobian matrix when current performs well. The numerical results show that is more robust faster than traditional optimization such as Levenberg–Marquardt (a variant methods, built-in subroutine fsolve.m MATLAB R2020a environment). time about 1/8 1/50 fsolve. Furthermore, it also proves global convergence local superlinear under some standard assumptions.