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《Journal of Southeast Univwrsity(Natural Science Edition)》 2001-05
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Convergence of Gauss-Newton's Method

Zhang WenhongLi Chong (Department of Applied Mathematics, Southeast University, Nanjing 210096, China)  
et f:R n→R m be a nonlinear Frechet differentiable map, where mn . The authors investigate the convergence problem of Gauss-Newton's method x n+1 =x n-[JB([]f[KG*7]′(x n) T f[KG*7]′(x n)[JB)]] -1 f[KG*7]′(x n) T f(x n), n=0,1,2,... for finding the approximation solution of nonlinear least squares problems min F(x)=[SX(]1[]2[SX)]f(x) T f(x). Under the hypothesis that JP2 f[KG*7]′(x 0) -1 exists and the derivative of f in B(x 0,r) satisfies the Lipschitz continuous: [JB(=]f[KG*7]′(x)-f[KG*7]′(x′)[JB)=]≤γ[JB(=]x-x′[JB)=], x,x′∈B(x 0,r). With a criterion on the initial value c=[JB(=]f(x 0)[JB)=], β=[JB(=][JB([]f[KG*7]′ T (x 0)f[KG*7]′(x 0)[JB)]] -1 JB) f[KG*9]′ JB( (x 0) T [JB)=], β 2cγ1/10 JP , we judge that the {x n} produced by Gauss-Newton's method is convergent to x * . Thereby the convergence theorem of Gauss-Newton's method is obtained.
【Fund】: 国家自然科学基金资助项目 ( 199710 13);; 江苏省自然科学基金资助项目 (BK990 0 1)
【CateGory Index】: O242.2
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