Fast Balanced
Stochastic Truncation Via A Quadratic Extension of the Alternating
Direction Implicit Iteration
Fast Balanced
Stochastic Truncation Via A Quadratic Extension of the Alternating
Direction Implicit Iteration
N. Wong and V. Balakrishnan
In Proc. Int. Conf. on Computer-Aided Design (ICCAD) ,
San Jose, CA, November 2005
Abstract: Balanced truncation (BT) model order reduction
(MOR) is known for its superior accuracy and computable error
bounds. Balanced stochastic truncation (BST) is a particular BT
procedure that provides a general, structure-independent MOR framework
to preserve both passivity and stability of original models. Its
application toward large scale systems, however, has been limited by
the complexity of solving large size continuous time algebraic Riccati
equations (CAREs). This paper introduces a novel quadratic extension
of the alternating direction implicit (ADI) iteration, called QADI,
that efficiently solves a CARE. A Cholesky factor variant of QADI,
called CFQADI, further exploits low rank matrices and and produces
solution in factor form that greatly accelerates BST. Remarkable
efficiency of the proposed BST/(CF)QADI integration is demonstrated
with numerical examples.
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