通俗化延续牛顿方法和信托区域未定系统更新战略 (Generalized continuation Newton methods and the trust-region updating strategy for the underdetermined system)

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

翻译：本文件考虑了普遍延续牛顿法和托拉斯区域非线性方程式系统未定体系更新战略;此外,为了提高计算效率,新方法在目前的雅各布矩阵运行良好时不会更新雅各布矩阵;数字结果显示,新方法比传统的优化方法,如Levenberg-Marquardt方法(信任区域方法的一种变体,MATLAB R2020a环境的内置次例法fSolve.m)更强大、更快。新方法的计算时间大约是FSolve的1/8至1/50。此外,它也证明了某些标准假设下的新方法的全球趋同和本地超线性趋同。