Using Krylov-Subspace Methods for Reduced-Order Modeling
by
Roland W. Freund
Bell Laboratories, Lucent Technologies

Krylov-subspace methods, most notably the Lanczos algorithm and the Arnoldi process, have long been recognized as powerful tools for the iterative solution of large systems of linear equations and for large-scale eigenvalue computations. In recent years, Krylov-subspace algorithms have also emerged as the methods of choice for reduced-order modeling of large-scale linear dynamical systems. These recent developments have been driven mostly by the need for efficient reduced-order modeling techniques in the simulation of integrated electronic circuits.

In this talk, we explain why and how Krylov-subspace methods are employed to generate reduced-order models of large-scale linear dynamical systems, especially those arising in VLSI circuit simulation. We discuss various desirable and in part conflicting properties of the reduced-order models, such as high approximation accuracy, stability, and passivity, and show how to achieve these properties by means of Krylov-subspace iterations. Numerical results for a variety of examples from VLSI circuit simulation are presented.

Roland W. Freund's homepage

Date received: February 2, 2000