Krylov Subspace Projection Methods for Model Reduction
D.C. SorensenRice University, Houston
Thursday July 22, 3.00 a.m. Parallel Algorithms Seminar CERFACS Conference Room
Abstract : This talk will survey some numerical techniques for obtaining reduced order
models of large state space systems of the form
\dot{x} = Ax + Bu
y = Cx
where $ A,B,C$ are $n\times n$, $n \times m $ and $m \times n$ matrices,
and $x,y,u$ are vector functions of time with dimensions $n,m$ and $m$.
Such systems arise in the analysis of large linear circuits and also
through discretization of control systems involving time dependent partial
differential equations.
Computational cost motivates the development of reduced order models
which accurately approximate the response $y$ of the full system for a
given input $u$. We shall survey various Krylov subspace projection
techniques and discuss connections between the Lanczos algorithm and
classic moment theory. We shall also discuss approches to obtaining
partial balanced realizations (or reduced models). These have potential
to provide two important features that are usually lacking in existing
model reduction schemes.
1. Straightforward extension from single input single output (SISO) to
multiple input multiple output (MIMO) systems.
2. Rigorous bounds are available on the $\Hinf$ norm of the difference
between the full order system and the reduced order system in terms of
the Hankel singular values neglected by the reduced order system.
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