Singular Value Factorization for Universal Extended Matrix

doi:10.3969/j.issn.0372-2112.2012.08.007

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Singular Value Factorization for Universal Extended Matrix

更新时间：2025-07-08

- Singular Value Factorization for Universal Extended Matrix
- Acta Electronica Sinica Vol. 40, Issue 8, Pages: 1539-1543(2012)
- 作者机构：
  
  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
  2. 重庆工商大学数学与统计学院,重庆,400067
- 作者简介：
- 基金信息：
- DOI：10.3969/j.issn.0372-2112.2012.08.007
  CLC： TN911.7
- Published：2012
- 稿件说明：
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Singular Value Factorization for Universal Extended Matrix[J]. Acta Electronica Sinica, 2012, 40(8): 1539-1543.
DOI：

Singular Value Factorization for Universal Extended Matrix[J]. Acta Electronica Sinica, 2012, 40(8): 1539-1543. DOI： 10.3969/j.issn.0372-2112.2012.08.007.

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.

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.

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Related Institution

Dept.of Automation,Tsinghua University,State Key Laboratory of Intelligent Technology and Systems

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Dept.of AutomationTsinghua UniversityState Key Laboratory of Intelligent Technology and SystemsBeijing 100084China

Dept.of Mathematical SciencesTsinghua UniversityBeijing 100084China

经济社会应用统计重庆市重点实验室

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