Structured total least squares and L2 approximation problems

AbstractIt is shown how structured and weighted total least squares and L2 approximation problems lead to a “nonlinear” generalized singular value decomposition. An inverse iteration scheme to find a (local) minimum is proposed. The emphasis of the paper is not on the convergence analysis of the algorithm; rather the purpose is to illustrate its use in numerous applications in systems and control, including total least squares with relative errors and/or fixed elements, inverse singular value problems, an errors-in-variables variant of the Kalman filter, impulse response realization from noisy data, H2 model reduction, H2 system identification, and calculating the largest stability radius of uncertain linear systems. Several numerical examples are given