Low Rank Approximation Solution of a Class of Generalized Lyapunov Equation (Journal of Computational Mathematics, 2018)
In this paper, we consider the low rank approximation solution of a generalized Lyapunov equation which arises in the bilinear model reduction. By using the variation principle, the low rank approximation solution problem is transformed into an unconstrained optimization problem, and then we use the nonlinear conjugate gradient method with exact line search to solve the equivalent unconstrained optimization problem. Finally, some numerical examples are presented to illustrate the effectiveness of the proposed methods.
Keywords: Generalized Lyapunov equation; Bilinear model reduction; Low rank approximation solution; Numerical method.