Data-flow algorithms for parallel matrix computation
Communications of the ACM
A set of level 3 basic linear algebra subprograms
ACM Transactions on Mathematical Software (TOMS)
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)
A Parallel Algorithm for the Sylvester Observer Equation
SIAM Journal on Scientific Computing
GEMM-based level 3 BLAS: high-performance model implementations and performance evaluation benchmark
ACM Transactions on Mathematical Software (TOMS)
Algorithm 784: GEMM-based level 3 BLAS: portability and optimization issues
ACM Transactions on Mathematical Software (TOMS)
The Journal of Supercomputing
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)
A Block Algorithm for Matrix 1-Norm Estimation, with an Application to 1-Norm Pseudospectra
SIAM Journal on Matrix Analysis and Applications
Solution of the matrix equation AX + XB = C [F4]
Communications of the ACM
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
A Parallel Implementation of the Nonsymmetric QR Algorithm for Distributed Memory Architectures
SIAM Journal on Scientific Computing
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)
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
PARA '02 Proceedings of the 6th International Conference on Applied Parallel Computing Advanced Scientific Computing
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
Formal derivation of algorithms: The triangular sylvester equation
ACM Transactions on Mathematical Software (TOMS)
Design and evaluation of a TOP100 Linux Super Cluster system: Research Articles
Concurrency and Computation: Practice & Experience
Block variants of Hammarling's method for solving Lyapunov equations
ACM Transactions on Mathematical Software (TOMS)
Multishift Variants of the QZ Algorithm with Aggressive Early Deflation
SIAM Journal on Matrix Analysis and Applications
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
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
Parallel Algorithms for Triangular Periodic Sylvester-Type Matrix Equations
Euro-Par '08 Proceedings of the 14th international Euro-Par conference on Parallel Processing
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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Parallel ScaLAPACK-style algorithms for solving eight common standard and generalized Sylvester-type matrix equations and various sign and transposed variants are presented. All algorithms are blocked variants based on the Bartels--Stewart method and involve four major steps: reduction to triangular form, updating the right-hand side with respect to the reduction, computing the solution to the reduced triangular problem, and transforming the solution back to the original coordinate system. Novel parallel algorithms for solving reduced triangular matrix equations based on wavefront-like traversal of the right-hand side matrices are presented together with a generic scalability analysis. These algorithms are used in condition estimation and new robust parallel sep − 1-estimators are developed. Experimental results from three parallel platforms, including results from a mixed OpenMP/MPI platform, are presented and analyzed using several performance and accuracy metrics. The analysis includes results regarding general and triangular parallel solvers as well as parallel condition estimators.