超定方程组残量极小化的定向扰动最小二乘法

超定方程组残量极小化的定向扰动最小二乘法 DIRECTIONAL PERTURBATION LEAST-SQUARES METHOD OF MINIMIZING THE RESIDUAL OF AN OVERDETERMINED SYSTEM OF LINEAR EQUATIONS 杨曙光 Yang Shuguang 1 first-author 武汉大学数学系 武汉大学数学系 Department Of mathematics,Wuhan University Department Of mathematics,Wuhan University 本文提出一个所谓"定向扰动最小二乘法"的统一算法,它仅仅只用最小二乘技术就可以给出一个超定线性方程组的 L 2 、L ∞ 和 L p （1≤P < 2）模意义下的最优解。这对于那些由实验数据求曲线拟合公式（统计学中的回归分析或参数估计）、建立数学模型、转子动力学中的平衡计算等自然科学和工程技术部门的实际问题有着广泛的应用。 A lot of curve fiting problem of experiment data lead to Solution of an Overdetermined system of Linear equations.But it is not clear prior that the data are either exact or Contaminated with errors of an unknown natu re.Consequently we not only need to use L 2 —solution of the system but also L ∞ or L p solution.In this paper we propose an universal algorithm called the Directional Perturbation Least-Squares（DPLS）Algorithm which can give optimal solutions of an overdetermined system of linear equations in L 2 ,L ∞ L p （1≤p < 2）norms using only L.S.techniques.Theoretical principle of the algorithm is given in §3.Two examples are given in the end. 最小二乘法 超定线性方程组 定向扰动 Lp 模极小化 曲线拟合 least squares method overdetermined system of linear equ ations directional perturbation minimizing of residual in Lp norm curve fitting 1990-03-01 2021-04-01 3