TIME-VARYING LOSSLESS SYSTEMS AND THE INVERSION OF LARGE STRUCTURED MATRICES

In the inversion of large matrices, direct methods might give undesire d 'unstable' results. Valuable insight into the mechanism of this effe ct is obtained by viewing the matrix as the input-output operator of a time-varying system, which allows to translate 'unstable' into 'anti- causal' but bounded inverses. Inner-outer factorizations and other los sless factorizations from system theory play the role of QR factorizat ions. They are computed by state space techniques and lead to a sequen ce of QR factorizations on time-varying realization matrices. We show how several such results can be combined to solve the inversion proble m.