Solving tridiagonal systems on ensemble architectures
SIAM Journal on Scientific and Statistical Computing
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
The Stanford Dash Multiprocessor
Computer
Optimal broadcast and summation in the LogP model
SPAA '93 Proceedings of the fifth annual ACM symposium on Parallel algorithms and architectures
A parallel version of the cyclic reduction algorithm on a hypercube
Parallel Computing
LogP: a practical model of parallel computation
Communications of the ACM
Optimal and near-optimal algorithms for k-item broadcast
Journal of Parallel and Distributed Computing
Monsoon: an explicit token-store architecture
ISCA '90 Proceedings of the 17th annual international symposium on Computer Architecture
Analysis and Design of Parallel Algorithms: Arithmetic and Matrix Problems
Analysis and Design of Parallel Algorithms: Arithmetic and Matrix Problems
Optimal and efficient algorithms for summing and prefix summing on parallel machines
Journal of Parallel and Distributed Computing
Optimal Parallel Algorithms for Solving Tridiagonal Linear Systems
Euro-Par '97 Proceedings of the Third International Euro-Par Conference on Parallel Processing
Parallel solution of large symmetric tridiagonal linear systems
Parallel Computing
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The problem of solving tridiagonal linear systems on parallel distributed-memory environments is considered in this paper. In particular, two common direct methods for solving such systems are considered: odd-even cyclic reduction and prefix summing. For each method, a variety of lower bounds on execution time for solving tridiagonal linear systems are presented. Specifically, lower bounds are presented that (a) hold when the number of data items per processor is bounded, (b) are general lower bounds, and (c) for specific data layouts commonly used in designing parallel algorithms to solve tridiagonal linear systems. Furthermore, algorithms are presented that have running times within a constant factor of the lower bounds provided. Lastly, a comparison of bounds for odd-even cyclic reduction and prefix summing is given.