摘要
考虑求解非线性最小二乘问题的不精确高斯—牛顿法。给出了在高斯—牛顿方程组不精确求解条件下，搜索方向Ｓ（ｎ）是下降方向和确保方法收敛的条件。文章还证明了，如果高斯—牛顿方程组的求解是渐近精确的，则对充分大的Ｋ，步长αｋ＝１是可接受的，且方法的局部收敛率是超线性的。
Abstract The inexact damped Gauss Newton method x k+1 =x k+α ks k, with M(x k)s k=-g(x k)+ψ k, ‖ψ k‖/‖g(x k)‖≤ε k for solving nonlinear least squares problems is considered in this paper. It is proved that if the forcing seguence (ε k) is uniformly less than one and {M(x k)} is uniformly bounded, then the search directions s k at each iteration is a descent direction and the method is convergent. Furthermore if ε k→0 then for zero residual problems, the unit step length α k=1 is acceptable for sufficiently large k and the local rate of convergence is superlinear.
出处
《工程数学学报》
CSCD
北大核心
1997年第4期1-7,共7页
Chinese Journal of Engineering Mathematics
