Iterative solution of the Lyapunov matrix equation
Applied Mathematics Letters
Robust and optimal control
A Cyclic Low-Rank Smith Method for Large Sparse Lyapunov Equations
SIAM Journal on Scientific Computing
Low-Rank Solution of Lyapunov Equations
SIAM Review
ICCAD '05 Proceedings of the 2005 IEEE/ACM International conference on Computer-aided design
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
Fast positive-real balanced truncation of symmetric systems using cross Riccati equations
Proceedings of the conference on Design, automation and test in Europe
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This paper presents a multi-shift generalization of the recently proposed quadratic alternating direction implicit (QADI) iteration. QADI and its Cholesky Factor (CF) variant, CFQADI, have been shown to be efficient ways of solving the large-scale algebraic Riccati equations (AREs) required in positive-real balanced truncation (PRBT). However, only their single-shift implementations have been considered so far. Using linear fractional transformation (LFT), we present elegant multi-shift extensions of both QADI and CFQADI, thereby enabling even faster and more accurate PRBT.