Large matrix inversion using state space techniques

A new computational technique is presented by which large structured matrices can be inverted. The specified matrix is viewed as the input-output operator of a time-varying system. Recently developed state space algorithms which apply to such systems are then used to compute a QR factorization first and subsequently the inverse of the matrix, starting from a state realization of the matrix. The new algorithms apply in principle to any matrix. They are efficient if the structure of the matrix is such that the number of states of its time-varying state realization is small in comparison to its dimensions