Robust and optimal control
A Cyclic Low-Rank Smith Method for Large Sparse Lyapunov Equations
SIAM Journal on Scientific Computing
Computer Methods for Circuit Analysis and Design
Computer Methods for Circuit Analysis and Design
Efficient Approximate Balanced Truncation of General Large-Scale RLC Systems via Krylov Methods
ASP-DAC '02 Proceedings of the 2002 Asia and South Pacific Design Automation Conference
Passivity-preserving model reduction via a computationally efficient project-and-balance scheme
Proceedings of the 41st annual Design Automation Conference
Low-Rank Solution of Lyapunov Equations
SIAM Review
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
PRIMA: passive reduced-order interconnect macromodeling algorithm
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Guaranteed passive balancing transformations for model order reduction
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Efficient linear circuit analysis by Pade approximation via the Lanczos process
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Proceedings of the 43rd annual Design Automation Conference
Fast positive-real balanced truncation of symmetric systems using cross Riccati equations
Proceedings of the conference on Design, automation and test in Europe
Hierarchical Krylov subspace reduced order modeling of large RLC circuits
Proceedings of the 2008 Asia and South Pacific Design Automation Conference
Hierarchical Krylov subspace based reduction of large interconnects
Integration, the VLSI Journal
Wideband reduced modeling of interconnect circuits by adaptive complex-valued sampling method
Proceedings of the 2010 Asia and South Pacific Design Automation Conference
ACM Transactions on Design Automation of Electronic Systems (TODAES)
Decentralized and passive model order reduction of linear networks with massive ports
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
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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.