On perturbations of some constrained subspaces (Q1008676)

The authors consider perturbations of some of the subblocks in a \(1\times2\), \(2\times1\) and \(2\times2\) block matrix. Via singular value decompositions of these blocks, estimates are derived for bounding the corresponding perturbations of the associated subspaces of the blocks, and hence also of the whole matrix. These results are important in several constrained (total) least squares problems where only a subblock can be perturbed under some restrictions. For example to minimize a norm under certain rank constraints. These applications are not included in this paper though. They will be described in a subsequent one.