摘要
本文从普通奇异值分解出发 ,导出了具有行或列对称结构的矩阵 (即延拓矩阵 )的奇异值和奇异向量与原矩阵 (亦称母矩阵 )的奇异值和奇异向量的定量关系 ,并对延拓矩阵进行了简单的扰动分析 .理论分析和数值实验的结果表明 ,就一大类延拓矩阵而言 ,仅用母矩阵进行奇异值分解不但可以节省计算量和存储量 。
In this paper,based on the ordinary singular value decomposition,a quantitative correspondence of the singular values and singular vectors between the row or column symmetric matrix (namely,the extended matrix) and its original (a k a mother matrix) is derived,and the perturbation analysis for the extended matrix is provided accordingly.Theoretical predictions and numerical evidences indicate that,for a class of extended matrices,the singular value decomposition using the mother matrix rather than the extended matrix per se can save dramatically the memory and alleviate considerably the computational burden without loss of any numerical precision.
出处
《电子学报》
EI
CAS
CSCD
北大核心
2001年第3期289-292,共4页
Acta Electronica Sinica
基金
国家自然科学基金!(No .697750 0 9)
国防科技重点实验室基金!(No .97JS34 7 1 JW0 1 0 5)
关键词
奇异值分解
母矩阵
延拓矩阵
扰动分析
时频分布
信号处理
singular value decomposition
mother matrix
extended matrix
perturbation analysis
time frequency distribution
signal processing
