Parallel solution of triangular systems on distributed-memory multiprocessors
SIAM Journal on Scientific and Statistical Computing
The role of elimination trees in sparse factorization
SIAM Journal on Matrix Analysis and Applications
A unified geometric approach to graph separators
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Introduction to parallel computing: design and analysis of algorithms
Introduction to parallel computing: design and analysis of algorithms
Analyzing scalability of parallel algorithms and architectures
Journal of Parallel and Distributed Computing - Special issue on scalability of parallel algorithms and architectures
Highly Scalable Parallel Algorithms for Sparse Matrix Factorization
IEEE Transactions on Parallel and Distributed Systems
Computer Solution of Large Sparse Positive Definite
Computer Solution of Large Sparse Positive Definite
Isoefficiency: Measuring the Scalability of Parallel Algorithms and Architectures
IEEE Parallel & Distributed Technology: Systems & Technology
A distributed solution of sparse linear systems
A distributed solution of sparse linear systems
Fast and effective algorithms for graph partitioning and sparse-matrix ordering
IBM Journal of Research and Development - Special issue: optical lithography I
Highly Scalable Parallel Algorithms for Sparse Matrix Factorization
IEEE Transactions on Parallel and Distributed Systems
A static parallel multifrontal solver for finite element meshes
ISPA'06 Proceedings of the 4th international conference on Parallel and Distributed Processing and Applications
Parallel forward and back substitution for efficient power grid simulation
Proceedings of the International Conference on Computer-Aided Design
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A few parallel algorithms for solving triangular systems resulting from parallel factorization of sparse linear systems have been proposed and implemented recently. We present a detailed analysis of parallel complexity and scalability of the best of these algorithms and the results of its implementation on up to 256 processors of the Cray T3D parallel computer. It has been a common belief that parallel sparse triangular solvers are quite unscalable due to a high communication to computation ratio. Our analysis and experiments show that, although not as scalable as the best parallel sparse Cholesky factorization algorithms, parallel sparse triangular solvers can yield reasonable speedups in runtime on hundreds of processors. We also show that for a wide class of problems, the sparse triangular solvers described in this paper are optimal and are asymptotically as scalable as a dense triangular solver.