Balanced parametrization of classes of linear systems
SIAM Journal on Control and Optimization
Reduced-order modeling of large passive linear circuits by means of the SYPVL algorithm
Proceedings of the 1996 IEEE/ACM international conference on Computer-aided design
ScaLAPACK user's guide
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
A Cyclic Low-Rank Smith Method for Large Sparse Lyapunov Equations
SIAM Journal on Scientific Computing
Interconnect Analysis and Synthesis
Interconnect Analysis and Synthesis
Low Rank Solution of Lyapunov Equations
SIAM Journal on Matrix Analysis and Applications
MUMPS: A General Purpose Distributed Memory Sparse Solver
PARA '00 Proceedings of the 5th International Workshop on Applied Parallel Computing, New Paradigms for HPC in Industry and Academia
Approximation of Large-Scale Dynamical Systems (Advances in Design and Control) (Advances in Design and Control)
Parallel Implementation of LQG Balanced Truncation for Large-Scale Systems
Large-Scale Scientific Computing
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We discuss a parallel algorithm for the solution of large-scale generalized algebraic Riccati equations with dimension up to $\mathcal{O}(10^5)$. We survey the numerical algorithms underlying the implementation of the method, in particular, a Newton-type iterative solver for the generalized Riccati equation and an LR-ADI solver for the generalized Lyapunov equation. Experimental results on a cluster of Intel Xeon processors illustrate the benefits of our approach.