Fast Positive-Real Balanced Truncation Via Quadratic Alternating Direction Implicit Iteration
Fast Positive-Real Balanced Truncation Via Quadratic Alternating Direction Implicit Iteration
N. Wong and V. Balakrishnan
To appear in
IEEE Trans. Computer-Aided Design of Integrated Circuits and Systems
, 2007.
Abstract:
Balanced truncation (BT), as applied to date in model order reduction
(MOR), is known for its superior accuracy and computable error
bounds. Positive-real balanced truncation (PRBT) is a particular BT
procedure that preserves passivity and stability, and imposes no
structural constraints on the original state space. However, PRBT
requires solving two algebraic Riccati equations (AREs), whose
computational complexity limits its practical use in large-scale
systems. This paper introduces a novel quadratic extension of the
alternating direction implicit (ADI) iteration, called QADI, that
efficiently solves an ARE. A Cholesky factor version of QADI, called
CFQADI, exploits low-rank matrices and further accelerates PRBT.
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