[1]张文红,李冲.Gauss-Newton法的半局部收敛性[J].东南大学学报(自然科学版),2001,31(5):135-139.[doi:10.3969/j.issn.1001-0505.2001.05.029] 　Zhang Wenhong,Li Chong.Convergence of Gauss-Newton’s Method[J].Journal of Southeast University (Natural Science Edition),2001,31(5):135-139.[doi:10.3969/j.issn.1001-0505.2001.05.029] 点击复制 Gauss-Newton法的半局部收敛性() 分享到： var jiathis_config = { data_track_clickback: true };

31

2001年第5期

135-139

2001-09-20

文章信息/Info

Title:
Convergence of Gauss-Newton’s Method

Author(s):
Department of Applied Mathematics, Southeast University, Nanjing 210096, China)

Keywords:

O214.7
DOI:
10.3969/j.issn.1001-0505.2001.05.029

Abstract:
Let f:Rn→Rm be a nonlinear Frechet differentiable map, where m>n. The authors investigate the convergence problem of Gauss-Newton’s method xn+1=xn-[f ′(xn)Tf ′(xn)]-1f ′(xn)Tf(xn), n=0,1,2,… for finding the approximation solution of nonlinear least squares problems minF(x)=1/2f(x)Tf(x). Under the hypothesis that f ′(x0)-1 exists and the derivative of f in B(x0,r) satisfies the Lipschitz continuous: =f ′(x)-f ′(x′)=≤γ=x-x′=, x,x′∈B(x0,r). With a criterion on the initial value c==f(x0)=, β==[f ′T(x0)f ′(x0)]-1 f ′(x0)T=, β2cγ<1/10, we judge that the {xn} produced by Gauss-Newton’s method is convergent to x*. Thereby the convergence theorem of Gauss-Newton’s method is obtained.

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