DISPLACEMENT STRUCTURE OF PSEUDOINVERSES

A matrix or a linear operator A is said to possess an UV-displacement structure if rank(AU - VA) is small compared with the rank of A. Estim ates for tbe rank of A(dagger)V - UA(dagger) and more general displace ments of A(dagger) are presented, where A(dagger) is the pseudoinverse of A. The general results are applied to close-to-Toeplitz, close-to- Vandermonde, and generalized Cauchy matrices, Bezoutians, Toeplitz and Hankel operators, singular integral operators, and integral operators with displacement kernel. This leads to formulas for At which can be used for the fast computation of pseudosolutions. For Vandermonde matr ices the exact displacement rank of A(dagger) is evaluated. It turns o ut that this rank is not always small.