关于样本相关系数矩阵等行和分解算法的改进  

Improvement on the Algorithm of Equal Line Sum Decomposition for Sample Correlation Coefficient Matrix

作　　者：柳毅[1] 柳力[2] 

机构地区：[1]吉林铁道职业技术学院,吉林132002 [2]吉林市广播电视大学,吉林132002

出　　处：《武汉理工大学学报》2009年第12期165-168,共4页Journal of Wuhan University of Technology

摘　　要：在涉及生物群体或企业生产过程控制的抽样检验中,所得样本不是简单随机样本的情况是经常出现的。对这类正态总体下的非独立样本进行假设检验,首先要通过变换的方法将样本转换为另一正态总体的简单随机样本,而实现这个转换的关键是对非独立样本的相关系数矩阵作"等行和分解"。因此,设法寻求对样本相关系数矩阵实施等行和分解的有效算法并使其实用化,是把基于正态总体非独立样本的假设检验理论用于解决实际问题的关键。有学者提出了分解样本相关系数矩阵的一种算法,该算法尚需改进。改进的算法避免了原算法中所涉及的矩阵分解和求逆,代之以容易机上实现的矩阵或向量的乘法。Concerning the samples from biological group or enterprise producing process control, usually the samples are not random ones . For the hypothesis testing of normal totality on dependent sample, first of all, by means of transformation, samples are transformed to another normal totality at random and the key to this transformation lies in equal line sum decomposition for the sample correlation coefficient matrix. Therefore, to seek effective method for the decomposition and make it practical is the key to the hypothesis test. In Paper 3,, the algorithm for this is first put forward. In this paper, the algorithm of Paper 3 is improved. The improved algorithm calculates only multiplication of matrix or vector without calculating decomposition matrix and inverse matrix.

关 键 词：假设检验 正定矩阵 等行和分解 算法 

分 类 号：O241.6[理学—计算数学]