An algorithm for model reduction of large-scale systems via equality constrained least squares

A new SVD-Krylov based method is proposed, which is equivalent to compute an equality constrained leastsquares problem. The reduced model matches the first r + i Markov parameters of the full order model. Based on the rational equality constrained least-squares method, an iterative algorithm for H₂ model reduction is prensented. Moreover, both algorithms of IRKA ( An Iterative Rational Krylov Algorithm)and ISRK(An iterative SVD-rational Krylov based model reduction method) turns out to be two special cases of the proposed algorithm. The algorithm is numerically effective and suited for large-scale problem, which can be verified in the numerical examples.