Structure and perturbation analysis of truncated SVDs for column-partitioned matrices (Q2719196)

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 authors assume that \(A\) is partitioned in columns and discuss the relation between the SVD of \(A\) and of its block columns. NEWLINENEWLINENEWLINEIn the first half of the text, 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 SVDs of its block columns is complemented by certain bounds and the analysis of the low-rank-plus-shift structure is performed in more detail.