Parallel algorithms for LQ optimal control of discrete-time periodic linear systems
Journal of Parallel and Distributed Computing
PARA '02 Proceedings of the 6th International Conference on Applied Parallel Computing Advanced Scientific Computing
Block algorithms for reordering standard and generalized Schur forms
ACM Transactions on Mathematical Software (TOMS)
Block variants of Hammarling's method for solving Lyapunov equations
ACM Transactions on Mathematical Software (TOMS)
Accelerating the complex Hessenberg QR algorithm with the CSX600 floating-point coprocessor
PDCS '07 Proceedings of the 19th IASTED International Conference on Parallel and Distributed Computing and Systems
Prospectus for the next LAPACK and ScaLAPACK libraries
PARA'06 Proceedings of the 8th international conference on Applied parallel computing: state of the art in scientific computing
Parallel variants of the multishift QZ algorithm with advanced deflation techniques
PARA'06 Proceedings of the 8th international conference on Applied parallel computing: state of the art in scientific computing
PARA'06 Proceedings of the 8th international conference on Applied parallel computing: state of the art in scientific computing
ACM Transactions on Mathematical Software (TOMS)
A Novel Parallel QR Algorithm for Hybrid Distributed Memory HPC Systems
SIAM Journal on Scientific Computing
Eigenvalue perturbation bounds for Hermitian block tridiagonal matrices
Applied Numerical Mathematics
Chasing Bulges or Rotations? A Metamorphosis of the QR-Algorithm
SIAM Journal on Matrix Analysis and Applications
On aggressive early deflation in parallel variants of the QR algorithm
PARA'10 Proceedings of the 10th international conference on Applied Parallel and Scientific Computing - Volume Part I
Journal of Computational and Applied Mathematics
An iterative method for single and vertically stacked semiconductor quantum dots simulation
Mathematical and Computer Modelling: An International Journal
dqds with Aggressive Early Deflation
SIAM Journal on Matrix Analysis and Applications
Parallel reduction to hessenberg form with algorithm-based fault tolerance
SC '13 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
Optimally packed chains of bulges in multishift QR algorithms
ACM Transactions on Mathematical Software (TOMS)
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Aggressive early deflation is a QR algorithm deflation strategy that takes advantage of matrix perturbations outside of the subdiagonal entries of the Hessenberg QR iterate. It identifies and deflates converged eigenvalues long before the classic small-subdiagonal strategy would. The new deflation strategy enhances the performance of conventional large-bulge multishift QR algorithms, but it is particularly effective in combination with the small-bulge multishift QR algorithm. The small-bulge multishift QR sweep with aggressive early deflation maintains a high rate of execution of floating point operations while significantly reducing the number of operations required.