Alternating direction algorithm for optimal ℋ2 model reduction

In this paper, we propose an alternating direction algorithm (ADA) to solve the optimal ℋ₂ model reduction problem. The main idea of the proposed algorithm is to approximate the cost function locally by two quadratic functions at each iterative step, and obtain the solution by linear searching on the Grassmann manifold. The proposed algorithm preserves stability of the system and guarantee a decrease in the ℋ2 error at each iteration step. It is suitable for the reduction of large-scale systems. Numerical examples demonstrate the approximation accuracy and the computational efficiency of the proposed algorithm.