The computation and communication complexity of a parallel banded system solver
ACM Transactions on Mathematical Software (TOMS)
Direct methods for sparse matrices
Direct methods for sparse matrices
Optimizing tridiagonal solvers for alternating direction methods on Boolean cube multiprocessors
SIAM Journal on Scientific and Statistical Computing
Efficient Tridiagonal Solvers on Multicomputers
IEEE Transactions on Computers
Application and accuracy of the parallel diagonal dominant algorithm
Parallel Computing
Parallel Computing - Special issue on applications: parallel computing in regional weather modeling
A Fast Direct Solution of Poisson's Equation Using Fourier Analysis
Journal of the ACM (JACM)
An Efficient Parallel Algorithm for the Solution of a Tridiagonal Linear System of Equations
Journal of the ACM (JACM)
A Parallel Method for Tridiagonal Equations
ACM Transactions on Mathematical Software (TOMS)
Parallel Computers Two: Architecture, Programming and Algorithms
Parallel Computers Two: Architecture, Programming and Algorithms
Scalability of Parallel Algorithm-Machine Combinations
IEEE Transactions on Parallel and Distributed Systems
Performance Considerations of Shared Virtual Memory Machines
IEEE Transactions on Parallel and Distributed Systems
Fast tridiagonal solvers on the GPU
Proceedings of the 15th ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming
Journal of Parallel and Distributed Computing
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Abstract--A new method, namely, the Parallel Two-Level Hybrid (PTH) method, is developed to solve tridiagonal systems on parallel computers. PTH has two levels of parallelism. The first level is based on algorithms developed from the Sherman-Morrison modification formula, and the second level can choose different parallel tridiagonal solvers for different applications. By choosing different outer and inner solvers and by controlling its two-level partition, PTH can deliver better performance for different applications on different machine ensembles and problem sizes. In an extreme case, the two levels of parallelism can be merged into one, and PTH can be the best algorithm otherwise available. Theoretical analyses and numerical experiments indicate that PTH is significantly better than existing methods on massively parallel computers. For instance, using PTH in a fast Poisson solver results in a 2-folds speedup compared to a conventional parallel Poisson solver on a 512 nodes IBM machine. When only the tridiagonal solver is considered, PTH is over 10 times faster than the currently used implementation.