On a block implementation of Hessenberg multishift QR iteration
International Journal of High Speed Computing
SIAM Journal on Matrix Analysis and Applications
Deferred shifting schemes for parallel QR methods
SIAM Journal on Matrix Analysis and Applications
Shifting strategies for the parallel QR algorithm
SIAM Journal on Scientific Computing
Theory of Decomposition and Bulge-Chasing Algorithms for the Generalized Eigenvalue Problem
SIAM Journal on Matrix Analysis and Applications
A Perturbation Analysis of the Generalized Sylvester Equation $(AR - LB, DR - LE) = (C, F)$
SIAM Journal on Matrix Analysis and Applications
ACM Transactions on Mathematical Software (TOMS)
Parallelizing the QR algorithm for the unsymmetric algebraic eigenvalue problem: myths and reality
SIAM Journal on Scientific Computing
ScaLAPACK user's guide
Using Level 3 BLAS in Rotation-Based Algorithms
SIAM Journal on Scientific Computing
Bulge Exchanges in Algorithms of QR Type
SIAM Journal on Matrix Analysis and Applications
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
Blocked algorithms and software for reduction of a regular matrix pair to generalized Schur form
ACM Transactions on Mathematical Software (TOMS)
The Multishift QR Algorithm. Part I: Maintaining Well-Focused Shifts and Level 3 Performance
SIAM Journal on Matrix Analysis and Applications
The Multishift QR Algorithm. Part II: Aggressive Early Deflation
SIAM Journal on Matrix Analysis and Applications
ACM Transactions on Mathematical Software (TOMS)
ACM Transactions on Mathematical Software (TOMS)
PARA '96 Proceedings of the Third International Workshop on Applied Parallel Computing, Industrial Computation and Optimization
A ScaLAPACK-Style Algorithm for Reducing a Regular Matrix Pair to Block Hessenberg-Triangular Form
PARA '98 Proceedings of the 4th International Workshop on Applied Parallel Computing, Large Scale Scientific and Industrial Problems
Parallel Two-Stage Reduction of a Regular Matrix Pair to Hessenberg-Triangular Form
PARA '00 Proceedings of the 5th International Workshop on Applied Parallel Computing, New Paradigms for HPC in Industry and Academia
Parallel Algorithms for Triangular Sylvester Equations: Design, Scheduling and Saclability Issues
PARA '98 Proceedings of the 4th International Workshop on Applied Parallel Computing, Large Scale Scientific and Industrial Problems
Parallel Implementation of the Nonsymmetric QR Algorithm forDistributed Memory Architectures
Parallel Implementation of the Nonsymmetric QR Algorithm forDistributed Memory Architectures
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
ACM Transactions on Mathematical Software (TOMS)
A Novel Parallel QR Algorithm for Hybrid Distributed Memory HPC Systems
SIAM Journal on Scientific Computing
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A parallel three-stage algorithm for reduction of a regular matrix pair (A, B) to generalized Schur from (S, T) is presented. The first two stages transform (A, B) to upper Hessenberg-triangular form (H, T) using orthogonal equivalence transformations. The third stage iteratively reduces the matrix in (H, T) form to generalized Schur form. Algorithm and implementation issues regarding the single-/double-shift QZ algorithm are discussed. We also describe multishift strategies to enhance the performance in blocked as well as in parallell variants of the QZ method.