Journal Article10.1137/0912044
Parallel algorithms for banded linear systems
TL;DR: A partitioned Gaussian elimination algorithm with partial pivoting which is suitable for multiprocessors with small to moderate numbers of processing elements is described, which is more complex than those which have been proposed for diagonally dominant and symmetric positive-definite systems.
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Abstract: A partitioned Gaussian elimination algorithm with partial pivoting which is suitable for multiprocessors with small to moderate numbers of processing elements is described. It is only assumed that the system is nonsingular; hence the submatrices in the chosen partitioning may be rank-deficient and this makes the algorithm more complex than those which have been proposed for diagonally dominant and symmetric positive-definite systems. Operation counts and stability are examined. Some numerical results obtained on Alliant FX/8 and Sequent Balance multiprocessors are presented.
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Citations
Conjugate Gradient Methods for Toeplitz Systems
Raymond H. Chan,Michael K. Ng +1 more
TL;DR: Some of the latest developments in using preconditioned conjugate gradient methods for solving Toeplitz systems are surveyed, finding that the complexity of solving a large class of $n-by-n$ ToePlitz systems is reduced to $O(n \log n)$ operations.
A High Throughput FPGA-Based Floating Point Conjugate Gradient Implementation for Dense Matrices
TL;DR: This article presents a widely parallel and deeply pipelined hardware CG implementation, targeted at modern FPGA architectures, particularly suited for accelerating multiple small-to-medium-sized dense systems of linear equations and can be used as a stand-alone solver or as building block to solve higher-order systems.
Fast band-Toeplitz preconditioners for Hermitian Toeplitz systems
TL;DR: It is shown that the condition number of systems preconditioned by the band-Toeplitz matrices are $O(1)$ for f, with or without zeros, and when f is positive, the precONDitioned systems converge at the same rate as other well-known circulant preconditionsed systems.
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Solution of discrete-time optimal control problems on parallel computers *
Stephen J. Wright
- 01 Dec 1990
TL;DR: Local-convergent algorithms for discrete-time optimal control problems which are amenable to multiprocessor implementation are described and results from an implementation on the Alliant FX/8 are described.
•Dissertation
Automatic and interactive parallelization
Kathryn S. McKinley
- 01 Jan 1992
TL;DR: This dissertation provides automatic compilation techniques that tailor parallel algorithms to shared-memory multiprocessors with local caches and a common bus, and develops novel, general algorithms to transform loops that contain arbitrary conditional control flow that are applicable to complete programs.
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References
Solving tridiagonal systems on ensemble architectures
TL;DR: Partitioning the ensemble into subsets of processors is shown to be more efficient for the solution of multiple independent problems than pipelining the solutions over the entire ensemble.
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The computation and communication complexity of a parallel banded system solver
Duncan H. Lawrie,Ahmed H. Sameh +1 more
TL;DR: Presentation d'un algorithme pour resoudre les systemes lineaires definis positifs a bandes sur un multiprocesseur ou le nombre de processeurs p est plus petit que l'ordre du systeme n.
95
Multiprocessor Schemes for Solving Block Tridiagonal Linear Systems
Michael W. Berry,Ahmed H. Sameh +1 more
- 01 Sep 1988
TL;DR: Such schemes are presented, along with specific performance results on the Alliant FX/8 and CRAY X-MP/48, and the development of a candidate scheme for the multicluster CEDAR machine is the goal.
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Parallel algorithms for the solution of narrow banded systems
TL;DR: Two medium grain methods for a linear array of processors are considered, one of which is a generalization of the work of Wang, while the second is one-way dissection applied to a band matrix, generalized for partial pivoting.
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