求解线性最小二乘的欧拉预报修正算法  

The Euler Predictor Corrector Algorithm for Solving Linear Least Squares

作　　者：夏林林[1] 贺建[2] 吴开腾[3] 

机构地区：[1]四川师范大学数学与软件科学学院,四川成都610066 [2]西南石油大学理学院,四川成都610500 [3]内江师范学院四川省高等学校数值仿真重点实验室,四川内江641100

出　　处：《内江师范学院学报》2013年第2期22-24,共3页Journal of Neijiang Normal University

基　　金：国家自然科学基金(10872085);四川省教育厅(11ZA026);内江市科技支撑项目(11029)

摘　　要：将欧拉方法与预报-修正技术结合,提出了一种改进的迭代法-欧拉预报修正算法,用于解超定方程组的最小二乘问题.首先将线性最小二乘转化为一类常微分方程组,运用欧拉方法求解;然后将其迭代结果作为预报值,引入相应的步长参数,构造新的迭代公式对预报值进行修正,从而提高算法的精度;最后通过数值试验验证,该算法是有效可行的.In combination with the Euler method and predictor corrector technology, an improved iterative method, the Euler predictor corrector algorithm, is proposed, for solving the least squares problems of overdetermined equations. First, the linear least squares problem is transformed into a class of ordinary differential equations, whose solution is then determined by means of the Euler method; then taking its iterative result as the forecast value, the corresponding step parameter is adopted to construct the new iterative formula so as to correct the forecast value, thus to improve the precision of the algorithm, and at last numerical experiments are conducted to prove the feasibility and validity of the said algorithm.

关 键 词：欧拉方法 预报-修正 超定方程组 最小二乘问题 

分 类 号：O241[理学—计算数学]