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三种度量向量组数值线性相关性方法的关系
张华仁^1,2,李维国¹
(1.中国石油大学数学与计算科学学院,山东东营 257061;2.中国科学院青岛生物能源与过程研究所,山东青岛 266101)

摘要:

讨论度量向量组的相对相关性指标、线性相关指标和最小相对范数指标。证明线性相关性指标和相对相关性指标的等价性,并建立最小相对范数指标与线性相关性指标的关系表达式。应用实例结果验证了所得结论的正确性。

关键词: 数值线性相关性 Gram行列式秩

DOI：

分类号::O 241.6

文献标识码:A

基金项目:国家自然科学基金项目(60971132);教育部人才计划项目(K080810B)

Relationship of three methods for measuring numerical linear dependence of vectors

ZHANG Hua ren^1,2, LI Wei guo¹

(1.College of Mathematics and Computational Sciences in China University of Petroleum, Dongying 257061, China;2.Qingdao Institute of BioEnergy and BioProcess Technology, Chinese Acedemy of Science, Qingdao 266101, China)

Abstract:

Relative dependence index, linear dependence index and the minimum relative norm index for measuring numerical linear dependence of vectors were researched. The equivalent property of the linear dependence index and the relative dependence index was proved and the relational expression of the minimal relative norm index and linear dependence index was founded. Numerical examples show the practicability of the results.

Key words: numerical linear dependence Gram determinant rank