A matrix rational Lanczos method for model reduction in large‐scale first‐ and second‐order dynamical systems

Abstract

Summary In the present paper, we describe an adaptive modified rational global Lanczos algorithm for model‐order reduction problems using multipoint moment matching‐based methods. The major problem of these methods is the selection of some interpolation points. We first propose a modified rational global Lanczos process and then we derive Lanczos‐like equations for the global case. Next, we propose adaptive techniques for choosing the interpolation points. Second‐order dynamical systems are also considered in this paper, and the adaptive modified rational global Lanczos algorithm is applied to an equivalent state space model. Finally, some numerical examples will be given.

Computational methods for model reduction in large-scale MIMO dynamical systems

“…As for the block Arnoldi-based methods, the last expression of the approximate solution could be used to obtain a truncated balanced approximation to get a low order dynamical sytem; see for example [18,88].…”

“…, s m , we refer to [1,50,51,69,156,157]. We notice that we can also define a rational version of the block Lanczos method [17,18,70].…”

“…The standard versions of these algorithms tend to create reduced order models that poorly approximate some frequency dynamics. To ameliorate this problem, rational Arnoldi and Lanczos algorithms [1,17,18,50,51,69,58] have been developed which produce reduced models that match the moments of the transfer function at different frequencies. The Krylov-subspace based methods have the advantages for large problems.…”