STRUCTURE AND PERTURBATION ANALYSIS OF TRUNCATED SVDs FOR COLUMN-PARTITIONED MATRICES.

In this paper we study truncated SVDs for column-partitioned matrices. In particular, we analyze the relation between the truncated SVDs of a matrix and the truncated SVDs of its submatrices. We give necessary and sufficient conditions under which a truncated SVD of a matrix can be constructed from those of its submatrices. We then present perturbation analysis to show that an approximate truncated SVD can still be computed even if the given necessary and sufficient conditions are only approximately satisfied. We also apply our general results to a class of matrices with the so-called low-rank-plus-shift structure. [ABSTRACT FROM AUTHOR]