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
Communication effect basic linear algebra computations on hypercube architectures
Journal of Parallel and Distributed Computing
Solving tridiagonal systems on ensemble architectures
SIAM Journal on Scientific and Statistical Computing
Optimum Broadcasting and Personalized Communication in Hypercubes
IEEE Transactions on Computers
Optimizing tridiagonal solvers for alternating direction methods on Boolean cube multiprocessors
SIAM Journal on Scientific and Statistical Computing
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)
Unified Architecture for Divide and Conquer Based Tridiagonal System Solvers
IEEE Transactions on Computers
Scalability versus execution time in scalable systems
Journal of Parallel and Distributed Computing
Parallel Minimal Norm Method for Tridiagonal Linear Systems
IEEE Transactions on Computers
A scalable parallel algorithm for periodic symmetric Toeplitz tridiagonal systems
Progress in computer research
A Parallel Two-Level Hybrid Method for Diagonal Dominant Tridiagonal Systems
IPDPS '02 Proceedings of the 16th International Parallel and Distributed Processing Symposium
PDRS: A Performance Data Representation System
IPDPS '00 Proceedings of the 15 IPDPS 2000 Workshops on Parallel and Distributed Processing
IEEE Transactions on Parallel and Distributed Systems
A Highly Parallel Algorithm for the Numerical Simulation of Unsteady Diffusion Processes
IPDPS '05 Proceedings of the 19th IEEE International Parallel and Distributed Processing Symposium (IPDPS'05) - Papers - Volume 01
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
Hi-index | 14.99 |
Three parallel algorithms, namely, the parallel partition LU (PPT) algorithm, the parallel partition hybrid (PPH) algorithm, and the parallel diagonal dominant (PDD) algorithm, are proposed for solving tridiagonal linear systems on multicomputers. These algorithms are based on the divide-and-conquer parallel computation model. The PPT and PPH algorithms support both pivoting and nonpivoting. The PPT algorithm is good when the number of processors is small; otherwise, the PPH algorithm is better. When the system is diagonal dominant, the PDD algorithm is highly parallel and provides an approximate solution which equals the exact solution within machine accuracy. Computation and communication complexities of the three algorithms are presented. All three methods have been implemented on a 64-node nCUBE-1 multicomputer. The analytic results closely match the results measured from the nCUBE-1 machine.