A class of parallel iterative methods implemented on multiprocessors
A class of parallel iterative methods implemented on multiprocessors
A bridging model for parallel computation
Communications of the ACM
s-step iterative methods for symmetric linear systems
Journal of Computational and Applied Mathematics
SIAM Journal on Scientific and Statistical Computing
Variants of BICGSTAB for matrices with complex spectrum
SIAM Journal on Scientific Computing
Applied Numerical Mathematics
GPBi-CG: Generalized Product-type Methods Based on Bi-CG for Solving Nonsymmetric Linear Systems
SIAM Journal on Scientific Computing
LogGP: incorporating long messages into the LogP model for parallel computation
Journal of Parallel and Distributed Computing
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
Accuracy of Two Three-term and Three Two-term Recurrences for Krylov Space Solvers
SIAM Journal on Matrix Analysis and Applications
GPBiCG(m, l): a hybrid of BiCGSTAB and GPBiCG methods with efficiency and robustness
Applied Numerical Mathematics - Developments and trends in iterative methods for large systems of equations—in memoriam Rüdiger Weiss
The Improved Quasi-minimal Residual Method on Massively Distributed Memory Computers
HPCN Europe '97 Proceedings of the International Conference and Exhibition on High-Performance Computing and Networking
Communication Cost Reduction for Krylov Methods on Parallel Computers
HPCN Europe 1994 Proceedings of the nternational Conference and Exhibition on High-Performance Computing and Networking Volume II: Networking and Tools
ICA3PP '02 Proceedings of the Fifth International Conference on Algorithms and Architectures for Parallel Processing
ICA3PP '02 Proceedings of the Fifth International Conference on Algorithms and Architectures for Parallel Processing
Accurate and Efficient Floating Point Summation
SIAM Journal on Scientific Computing
Communications of the ACM - Voting systems
SIAM Journal on Scientific Computing
Sparsity: Optimization Framework for Sparse Matrix Kernels
International Journal of High Performance Computing Applications
Optimization of sparse matrix-vector multiplication on emerging multicore platforms
Proceedings of the 2007 ACM/IEEE conference on Supercomputing
Accurate Floating-Point Summation Part I: Faithful Rounding
SIAM Journal on Scientific Computing
An improved parallel hybrid bi-conjugate gradient method suitable for distributed parallel computing
Journal of Computational and Applied Mathematics
Minimizing communication in sparse matrix solvers
Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis
Reducing Floating Point Error in Dot Product Using the Superblock Family of Algorithms
SIAM Journal on Scientific Computing
Optimizing collective communication on multicores
HotPar'09 Proceedings of the First USENIX conference on Hot topics in parallelism
Communication-avoiding krylov subspace methods
Communication-avoiding krylov subspace methods
Parallelism and error reduction in a high performance environment
Parallelism and error reduction in a high performance environment
A generalization of s-step variants of gradient methods
Journal of Computational and Applied Mathematics
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Eliminating synchronizations is one of the important techniques related to minimizing communications for modern high performance computing. This paper discusses principles of reducing communications due to global synchronizations in sparse iterative solvers on distributed supercomputers. We demonstrate how to minimize global synchronizations by rescheduling a typical Krylov subspace method. The benefit of minimizing synchronizations is shown in theoretical analysis and verified by numerical experiments. The experiments also show the local communications for some structured sparse matrix-vector multiplications and global communications in the underlying supercomputers increase in the order P^1^/^2^.^5 and P^4^/^5 respectively, where P is the number of processors.