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SIAM Journal on Matrix Analysis and Applications
Analysis and design of discrete linear control systems
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Linear robust control
Using MPI: portable parallel programming with the message-passing interface
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H2 optimal control
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SIAM Journal on Matrix Analysis and Applications
Using PLAPACK: parallel linear algebra package
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ScaLAPACK user's guide
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SIAM Journal on Scientific Computing
Using the Matrix Sign Function to Compute Invariant Subspaces
SIAM Journal on Matrix Analysis and Applications
A BLAS-3 Version of the QR Factorization with Column Pivoting
SIAM Journal on Scientific Computing
Indefinite-quadratic estimation and control: a unified approach to H2 and H∞ theories
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LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
Design and Analysis of Control Systems
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The Generalized Newton Iteration for the Matrix Sign Function
SIAM Journal on Scientific Computing
A Note On Parallel Matrix Inversion
SIAM Journal on Scientific Computing
Using hybrid CPU-GPU platforms to accelerate the computation of the matrix sign function
Euro-Par'09 Proceedings of the 2009 international conference on Parallel processing
Efficient model order reduction of large-scale systems on multi-core platforms
ICCSA'11 Proceedings of the 2011 international conference on Computational science and Its applications - Volume Part V
On the numerical solution of large-scale sparse discrete-time Riccati equations
Advances in Computational Mathematics
Accelerating model reduction of large linear systems with graphics processors
PARA'10 Proceedings of the 10th international conference on Applied Parallel and Scientific Computing - Volume 2
Accelerating BST methods for model reduction with graphics processors
PPAM'11 Proceedings of the 9th international conference on Parallel Processing and Applied Mathematics - Volume Part I
Unleashing CPU-GPU acceleration for control theory applications
Euro-Par'12 Proceedings of the 18th international conference on Parallel processing workshops
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We discuss a parallel library of efficient algorithms for the solution of linear-quadratic optimal control problems involving large-scale systems with state-space dimension up to O(104). We survey the numerical algorithms underlying the implementation of the chosen optimal control methods. The approaches considered here are based on invariant and deflating subspace techniques, and avoid the explicit solution of the associated algebraic Riccati equations in case of possible ill-conditioning. Still, our algorithms can also optionally compute the Riccati solution. The major computational task of finding spectral projectors onto the required invariant or deflating subspaces is implemented using iterative schemes for the sign and disk functions. Experimental results report the numerical accuracy and the parallel performance of our approach on a cluster of Intel Itanium-2 processors.