求解大型非线性最小二乘问题的组合有限差分Lanczos-Symm QR算法  

THE HYBRID FINITE DIFFERENCE LANCZOS-SYMM QR ALGORITHM FOR SOLVING LARGE NONLINEAR LEAST SQUARES PROBLEMS

作　　者：彭思图 

机构地区：[1]武汉市统计局,汉口430014

出　　处：《系统科学与数学》1992年第1期21-29,共9页Journal of Systems Science and Mathematical Sciences

基　　金：武汉钢铁学院科研基金

摘　　要：非线性最小二乘问题在实际中是广泛存在的,比如非线性回归及不相容非线性方程组的最小二乘解的问题等.这两类问题都可以用一个统一的形式表示.设 r:R^n→R^p(p≥n)是一个非线性映射,其意义是近似系统的误差.非线性最小二乘问题就是要找一个点 x~*∈R^n。For large nonlinear least squares problems,the hybrid finite difference Lanczos-Symm QRalgorithm presented in this paper is a better one in which the derivation is replaced by the finitedifference quotient,without iteration and storage of information of Hesse matrix,to obtain thedescent search direction.An convergence analysis of the algorithm is made and so a problemraised by P.Brown in 1987 is solved.

关 键 词：组合有限差分 L-SQR算法 收敛性 

分 类 号：O241.3[理学—计算数学]