This paper develops a computational approach to multivariable frequency domain curve fitting, based on two-norm minimization. The algorithm is specifically tailored to the identification of complex systems having a large number of parameters, and includes a sparse matrix method for reducing computation and memory requirements on large problems. The algorithm is also well-suited for identification of lightly damped systems such as flexible structures. The overall approach is successfully demonstrated on a high-order multivariable flexible structure experiment requiring the estimation of 780 parameters over a 100 Hz band width.