| Minimum norm method of analyzing ill-conditioned state of design matrix in estimation of parameters |
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| 引用本文： | 卢秀山,欧吉坤,宋淑丽,冯尊德. Minimum norm method of analyzing ill-conditioned state of design matrix in estimation of parameters[J]. 中国有色金属学会会刊, 2003, 13(3) |
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| 作者姓名： | 卢秀山 欧吉坤 宋淑丽 冯尊德 |
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| 作者单位： | School of Mapping and Surveying，Institute of Geodesy and Geophysics，School of Geo information Science and Technology，School of Geo information Science and Technology Wuhan University，Wuhan 430079，China，School of Geo information Science and Technology，Shandong University of Science and Technology，Tai′an 271019，China，The Chinese Academy of Sciences，Wuhan 430077，China，Shandong University of Science and Technology，Tai′an 271019，China，Shandong University of Science and Technology，Tai′an 271019，China |
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| 基金项目： | Project(4 0 14 40 18)supportedbytheNationalNaturalScienceFoundationofChina |
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| 摘 要： | 1 INTRODUCTIONThestructureofanormalmatrixNisofill con ditionedstateifitisofstrongmulti collinearity ,andtheNwillaffectthequalityofLSestimationofpa rameters[13] .Whentheill conditionedstateisseri ous ,changealittleintheseriesofobservationcausedbyerrorwillmakethecorrespondingestimatesofLSestimationchangealot.So ,objectivelydecidingthemulti collinearityoftheNisespeciallyimportant .ThematrixNconditionnumberisincommonlyusedtomeasurethemulti collinearity[4 6 ] .TheNcondi tionnumberisdefine…
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Minimum norm method of analyzing ill-conditioned state of design matrix in estimation of parameters |
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| LU Xiu shan ,,OU Ji kun ,SONG Shu li,FENG Zun de. Minimum norm method of analyzing ill-conditioned state of design matrix in estimation of parameters[J]. Transactions of Nonferrous Metals Society of China, 2003, 13(3) |
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| Authors: | LU Xiu shan OU Ji kun SONG Shu li FENG Zun de |
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| Affiliation: | LU Xiu shan 1,2,OU Ji kun 3,SONG Shu li2,FENG Zun de 2 |
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| Abstract: | 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 (αl), 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. |
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| Keywords: | estimation of parameters multi collinearity of matrix ill conditioned state of matrix norm of vector |
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