Linear algebra and its applications vol:188-189 pages:163-207
It 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, H-2 model reduction, H-2 system identification, and calculating the largest stability radius of uncertain linear systems. Several numerical examples are given.