Abstract
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. Estimates for the rank of A † V − UA † and more general displacements of A † are presented, where A † 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 A † which can be used for the fast computation of pseudosolutions. For Vandermonde matrices the exact displacement rank of A † is evaluated. It turns out that this rank is not always small.
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