Stable computation of the CS decomposition: Simultaneous bidiagonalization (Q2903107)

The CS-decomposition (CSD) simultaneously diagonalizes the blocks of a unitary matrix in a 2-by-2 block structure. There are quite a few applications of the CSD, e.g. principal angles in higher dimensional Euclidean geometry, perturbations of linear subspaces, canonical correlations in multivariate statistics, existence and computation of the generalized singular value decomposition (GSVD). In an earlier paper, the author had developed a new algorithm to calculate numerically the CSD. Here, its numerical stability is proved. In addition, a modification of this algorithm is given, which is numerically equivalent, but its analysis is more illuminating (according to the author).