Model reduction of state space systems via an implicitly restarted Lanczos method (Q1921318)

This paper uses a modified Lanczos method to derive a stable reduced order model for a single input-single output system described by the state space equation \(dx/dt =Ax +bu\), \(y=cx +du\). The basic assumption is that the matrix \(A\) is large, sparse and stable. The modification of the method lies in the fact that one uses oblique Krylov projectors to produce the model. The main interest of this approach is that the algorithm so obtained involves only inner-products and matrix-vector multiplications.