GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Parallel and distributed computation: numerical methods
Parallel and distributed computation: numerical methods
Microprocessing and Microprogramming
s-step iterative methods for (non)symmetric (in)definite linear systems
SIAM Journal on Numerical Analysis
A flexible inner-outer preconditioned GMRES algorithm
SIAM Journal on Scientific Computing
Reducing synchronization on the parallel Davidson method for the large sparse, eigenvalue problem
Proceedings of the 1993 ACM/IEEE conference on Supercomputing
Applied Numerical Mathematics
A Jacobi--Davidson Iteration Method for Linear EigenvalueProblems
SIAM Journal on Matrix Analysis and Applications
A hybrid block GMRES method for nonsymmetric systems with multiple right-hand sides
Proceedings of the 6th international congress on Computational and applied mathematics
Computer architecture (2nd ed.): a quantitative approach
Computer architecture (2nd ed.): a quantitative approach
The symmetric eigenvalue problem
The symmetric eigenvalue problem
A parallel algorithm for multilevel graph partitioning and sparse matrix ordering
Journal of Parallel and Distributed Computing
The grid: blueprint for a new computing infrastructure
The grid: blueprint for a new computing infrastructure
Jacobi--Davidson Style QR and QZ Algorithms for the Reduction of Matrix Pencils
SIAM Journal on Scientific Computing
Templates for the solution of algebraic eigenvalue problems: a practical guide
Templates for the solution of algebraic eigenvalue problems: a practical guide
Parallel preconditioning of a sparse eigensolver
Parallel Computing - Linear systems and associated problems
Scalable Parallel Computing: Technology,Architecture,Programming
Scalable Parallel Computing: Technology,Architecture,Programming
Numerical Linear Algebra for High Performance Computers
Numerical Linear Algebra for High Performance Computers
Lanczos Algorithms for Large Symmetric Eigenvalue Computations, Vol. 1
Lanczos Algorithms for Large Symmetric Eigenvalue Computations, Vol. 1
Multigrain Parallelism for Eigenvalue Computations on Networks of Clusters
HPDC '02 Proceedings of the 11th IEEE International Symposium on High Performance Distributed Computing
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Dynamic Load Balancing of an Iterative Eigensolver on Networks of Heterogeneous Clusters
IPDPS '03 Proceedings of the 17th International Symposium on Parallel and Distributed Processing
The university of Florida sparse matrix collection
ACM Transactions on Mathematical Software (TOMS)
Exploiting processor groups to extend scalability of the GA shared memory programming model
Proceedings of the 2nd conference on Computing frontiers
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Parallel iterative solvers are often the only means of solving large linear systems and eigenproblems. However, these solvers are usually implemented in a fine-grain manner and can incur significant performance penalties due to synchronization overheads on large MPPs. This problem is exacerbated in clusters of workstations (COWs) and SMPs that are interconnected via a hierarchy of networks. In this paper, we describe a novel scheme for hiding the synchronization overheads, and thus improving scalability, of block iterative solvers that employ a correction equation through an inner iterative method.Block methods are not only robust in the presence of eigenvalue multiplicities and multiple right-hand sides, but provide better latency tolerance by performing more floating-point operations between synchronizations. We take a different approach to inducing latency tolerance by increasing the granularity at which the correction equation is solved for each block vector. This is accomplished by splitting the processors into smaller subgroups which are then used to solve the correction for each block vector concurrently. The rest of the algorithm is still performed in fine grain. We call this combination of fine and coarse-grain parallelism multigrain parallelism.We implemented a multigrain, block Jacobi-Davidson algorithm for computing the extreme eigenvalues of a symmetric matrix. We obtained improvements of 45-50% over both the block and non-block implementations of the fine-grain method when testing on an IBM SP and on a collection of clusters of Sun workstations.