Parallelizing the QR algorithm for the unsymmetric algebraic eigenvalue problem: myths and reality
SIAM Journal on Scientific Computing
Matrix computations (3rd ed.)
Using PLAPACK: parallel linear algebra package
Using PLAPACK: parallel linear algebra package
ScaLAPACK user's guide
Computing rank-revealing QR factorizations of dense matrices
ACM Transactions on Mathematical Software (TOMS)
A BLAS-3 Version of the QR Factorization with Column Pivoting
SIAM Journal on Scientific Computing
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
Parallel Partial Stabilizing Algorithms for Large Linear Control Systems
The Journal of Supercomputing
Solution of the matrix equation AX + XB = C [F4]
Communications of the ACM
Specialized parallel algorithms for solving Lyapunov and Stein equations
Journal of Parallel and Distributed Computing
Singular Control Systems
A Note On Parallel Matrix Inversion
SIAM Journal on Scientific Computing
Parallel Implementation of the Nonsymmetric QR Algorithm forDistributed Memory Architectures
Parallel Implementation of the Nonsymmetric QR Algorithm forDistributed Memory Architectures
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We propose a parallel algorithm for stabilising large, discrete-time, linear control systems on a Beowulf cluster. Our algorithm first separates the Schur stable part of the linear control system using an inverse free iteration for the matrix disc function and then computes a stabilising feedback matrix for the unstable part. This stage requires the numerical solution of a Stein equation. This linear matrix equation is solved using the sign function method after applying a Cayley transformation to the original equation. The experimental results on a cluster composed of Intel PII processors and a Myrinet interconnection network show the parallelism and scalability of our approach.