解决非线性最小二乘问题两种方法.pdf

第21 卷　第5 期 青海大学学报(自然科学版) Vol.21 No.5 2003 年9 月 　　　　　　　　　Journal of Qinghai Universit 　　　　　　　　　 Sep .2003 张春晓 (, 　810016) :给出非线性最小二乘问题的两种计算方法, 利用非线性最小二乘法处理化学过程产量问 题, 到非线性估计参数。结果表明:非线性最小二乘法收敛性较好, 残差平方和较小。 :最小二乘法;牛顿法;拟牛顿法 :O241.6　　:A 　　:1006-8996(2003)05-0060-05 Two methods solving non-linear least square problem ZHANG Chun-xiao (Basic Research Department of Qinghai Universit , Xining 810016, China) Abstract :In this paper, the author gives two kinds of calculation methods on non linear least square prob- lem.The output problem in chemistr process is solved and non-liner least estimation parameters are got b appl ing non-liner least square method .The result shows not onl clearl good convergence of non- iner least square method, but also little residual square sum. Key words:least square method;Gauss-Newton method;Stable Factorized Gauss-Newton method 1　 : 1 m 2 1 2 minf (x)= ∑ r (x)= ‖r(x)‖i (1) x ∈R″ 2 i=1 2 n 　r(x)=(r (x), r (x), …, r (x)), r :R ※R, i=1, 2, …, m (m ≥n) 1 2 m i r(x), f (x): T g (x)= f (x)=A(x)r(x) (2) m 2 T 2 G(x)= f (x)=A(x)A(x)+∑ r (x) r (x)i i (3) i=1 A(X )∈Rm×nr (x)。 2 　 2.1 　—[1] —(Gauss-Newton Method), , , (1)。