自然水平函数在求解病态非线性组方程的阻尼牛顿法中的应用

Applications of Natural Level Functions in Damped Newton Method for Ill-conditioned Systems of Nonlinear Equations

利用自然水平函数,将众所周知的阻尼牛顿法进行推广,用于求解病态非线性方程组.算法具有下降性质.在适当条件下,建立了算法的全局和局部超线性/二阶收敛性.

By using the so-called'natural level functions',we extend the well-known damped Newton method to solve ill-conditioned systems of nonlinear equations.The descent property is well reserved by the algorithm.And under suitable conditions,we establish the global convergence and locally superlinear/quadratic convergence of the method.