Model-order reduction of large-scale kth-order linear dynamical systems via a kth-order Arnoldi method

Abstract

In this paper, we first introduce a kth-order Krylov subspace 𝒢 _n (A _j ; u) based on a square matrix sequence {A _j } and a vector u. Then we present a kth-order Arnoldi procedure for generating an orthonormal basis of 𝒢 _n (A _j ; u). By applying the projection technique, we derive a structure-preserving kth-order Arnoldi method for reduced-order modelling of the large-scale kth-order linear dynamical system. Applications to polynomial eigenvalue problems are also included. Numerical experiments report the effectiveness of this method.

Keywords:

• high-order linear system
• kth-order Krylov subspace
• kth-order Arnoldi procedure
• model-order reduction
• polynomial eigenvalue problem

2000 AMS Subject Classification :

• 65F10
• 65F15

Acknowledgements

Y. Lin was supported by Scientific Research Startup Foundation of Hunan University of Science and Engineering. L. Bao was supported by Scientific Research Startup Foundation of East China University of Science and Technology under grant YK0157110. Y. Wei was supported by the National Natural Science Foundation of China and Shanghai Education Committee. The authors would like to thank Professor Z. Bai for providing them with the examples and two referees for their helpful suggestions, which greatly improved the paper.