Zentralblatt MATH - REVIEW SUBMISSION FORM

Zentralblatt MATH HOME

Your review has been received.

Thank you very much.

(You may want so save a copy of this page for your files.)

Name:

Miloslav Znojil

Reviewer number:

9689

Email:

znojil@ujf.cas.cz

Item's zbl-Number:

DE 016 088 60X

Author(s):

Zhang, Zhenyue; Zha, Hongyuan

Shorttitle:

Structure and perturbation analysis of truncated SVD's for column-partitioned matrices

Source:

SIAM J. Matrix Anal. Appl. 22, No. 4, 1245-1262 (2001).

Classification:

Primary Classification:

15A18

Eigenvalues, singular values, and eigenvectors

Secondary Classification:

65F15

Eigenvalues, eigenvectors

Keywords:

singular value decomposition; block-column partitioning; re-construction of SVD from sub-SVD'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 low-rank-plus-shift structure is performed in more
detail.

Remarks to the editors:

(New formular )