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Name:  
Miloslav Znojil  
Reviewer number:  
9689  
Email:  
znojil@ujf.cas.cz  
Item's zblNumber:  
DE 016 088 60X  
Author(s):  
Zhang, Zhenyue; Zha, Hongyuan  
Shorttitle:  
Structure and perturbation analysis of truncated SVD's for columnpartitioned matrices  
Source:  
SIAM J. Matrix Anal. Appl. 22, No. 4, 12451262 (2001).  
Classification:  
Primary Classification:  
 
Secondary Classification:  
 
Keywords:  
singular value decomposition; blockcolumn partitioning; reconstruction of SVD from subSVD's; perturbation analysis  
Review:  
An approximation of a matrix A by another matrix of a lower rank is usually controlled by the so called singular value decomposition (SVD) of A. In the context of several possible applications the paper assumes that A is partitioned in columns and the relation between SVD of A and of its block columns is discussed. In the first half of the text, the necessary and sufficient conditions of an exact correspondence (reconstruction) are listed. The second half of the paper analyzes the situation where these conditions are perturbatively broken. Then, the reconstruction of the truncated SVD of A from the truncated SVD's of its block columns is complemented by certain bounds and the analysis of the lowrankplusshift structure is performed in more detail.  
Remarks to the editors:  