电子学报

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泛延拓矩阵的奇异值分解

袁晖坪   

  1. 重庆工商大学电子商务及供应链系统重庆市重点实验室, 重庆 400067; 重庆工商大学数学与统计学院, 重庆 400067
  • 收稿日期:2011-08-07 修回日期:2012-05-11 出版日期:2012-08-25 发布日期:2012-08-25
  • 作者简介:袁晖坪 男,1958年出生,重庆人,重庆工商大学教授,从事矩阵论、数字图像分析、模式识别等研究. E-mail:yhp@ctbu.edu.cn;hpyuan@163.com
  • 基金资助:

    国家自然科学基金(No.11001287);重庆市自然科学基金(No.CSTS 2005 BB 0243);电子商务及供应链系统重庆市重点实验室专项基金(No.2012ECSC0216)

Singular Value Factorization for Universal Extended Matrix

YUAN Hui-ping   

  1. Chongqing Key Laboratory of Electronic Commerce & Supply Chain System, Chongqing Technology and Business University, Chongqing, 400067, China; College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, 400067, China
  • Received:2011-08-07 Revised:2012-05-11 Online:2012-08-25 Published:2012-08-25

摘要: 从普通奇异值分解出发,导出了泛延拓矩阵的奇异值和奇异向量与母矩阵的奇异值和奇异向量间的定量关系,并对泛延拓矩阵作了简单的扰动分析、信号与图像分析.给出了泛延拓矩阵的奇异值分解与广义逆公式,极大地减少了它们的计算量与存储量,又不会降低数值精度.同时推广和优化了文献 的相应结果.

关键词: 泛延拓矩阵, 母矩阵, 奇异值分解, 扰动分析, 图像分析, 信号处理, 时频分布, 广义逆

Abstract: Based on the ordinary singular value factorization,a quantitative correspondence of the singular value and singular vectors between the universal extended matrix and its mother matrix is derived,and the perturbation analysis and image analysis for the universal extended matrix is provided accordingly.In addition,the formula of the singular value factorization and generalized inverse of universal extended matrix are given,which makes calculation easier and accurate.The results of Zou's SVD for extended Matrix are generalized.

Key words: universal extended matrix, mother matrix, singular value factorization, perturbation analysis, image analysis, signal processing, time-frequency distribution, generalized inverse

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