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
A Novel Parallel QR Algorithm for Hybrid Distributed Memory HPC Systems
SIAM Journal on Scientific Computing
Chasing Bulges or Rotations? A Metamorphosis of the QR-Algorithm
SIAM Journal on Matrix Analysis and Applications
Performance modeling and optimal block size selection for the small-bulge multishift QR algorithm
ISPA'06 Proceedings of the 4th international conference on Parallel and Distributed Processing 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
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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This paper presents a small-bulge multishift variation of the multishift QR algorithm that avoids the phenomenon of shift blurring, which retards convergence and limits the number of simultaneous shifts. It replaces the large diagonal bulge in the multishift QR sweep with a chain of many small bulges. The small-bulge multishift QR sweep admits nearly any number of simultaneous shifts---even hundreds---without adverse effects on the convergence rate. With enough simultaneous shifts, the small-bulge multishift QR algorithm takes advantage of the level 3 BLAS, which is a special advantage for computers with advanced architectures.