Minimum norm method of analyzing ill-conditioned state of design matrix in estimation of parameters

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	Minimum norm method of analyzing ill-conditioned state of design matrix in estimation of parameters
	Lu, X. S. ; Ou, J. K. ; Song, S. L. ; Feng, Z. D.
刊名	Transactions of Nonferrous Metals Society of China
	2003
期号	3 页码:724-728
中文摘要	The method of condition number is commonly used to diagnose a normal matrix N whether it is ill-conditioned state or not. For its shortcoming, a method to measure multi-collinearity of a matrix was put forward. The method is that implement Gram-Schmidt orthogonalizing process to column vectors of a design matrix A (a(i)), then calculate the norms of every vector before and after orthogonalization process and their corresponding ratio, and use the minimum ratio among the group of ratios to measure the multi-collinearity of A. According to the corresponding relationship between the multi-collinearity and the ill-conditioned state of a matrix, the method also studies and offers reference indexes weighing the ill-conditioned state of a matrix based on the relative norm. The remarkable characteristics of the method are that the measure of multi-collinearity has idiographic geometry meaning and clear lower and upper limit, the size of the measure reflects the multi-collinearity of column vectors objectively. It is convenient to study the reason that results in the matrix being multi-collinearity and to put forward solving plan according to the method which is summarized as the method of minimum norm and abbreviated as F method.
原文出处	://WOS:000183918700047
公开日期	2012-04-11
内容类型	期刊论文
源URL	[http://ir.whigg.ac.cn/handle/342008/3181]
专题	测量与地球物理研究所_其他_期刊论文
推荐引用方式 GB/T 7714	Lu, X. S.,Ou, J. K.,Song, S. L.,et al. Minimum norm method of analyzing ill-conditioned state of design matrix in estimation of parameters[J]. Transactions of Nonferrous Metals Society of China,2003(3):724-728.
APA	Lu, X. S.,Ou, J. K.,Song, S. L.,&Feng, Z. D..(2003).Minimum norm method of analyzing ill-conditioned state of design matrix in estimation of parameters.Transactions of Nonferrous Metals Society of China(3),724-728.
MLA	Lu, X. S.,et al."Minimum norm method of analyzing ill-conditioned state of design matrix in estimation of parameters".Transactions of Nonferrous Metals Society of China .3(2003):724-728.