Journal Article10.1109/TC.1982.1675924
A Practical Algorithm for the Solution of Triangular Systems on a Parallel Processing System
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TL;DR: An algorithm is presented for a more efficient and implementable solution of triangular systems on a parallel (SIMD) computer which requires 0(log (N) fewer processing cycles than the best previous results, where N is the system size.
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Abstract: An algorithm is presented for a more efficient and implementable solution of triangular systems on a parallel (SIMD) computer which requires 0(log (N)) fewer processing cycles than the best previous results, where N is the system size. We will also show that the data can be accessed and aligned in the same order of time using as many memory units as processors and Ω networks for data alignment. (Previous results dealing with this type of algorithm have not dealt in any detail with the problem of data access and alignment.)
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Citations
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Solution of Partial Differential Equations on Vector and Parallel Computers
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TL;DR: The intent is to point out attractive methods as well as areas where this class of computer architecture cannot be fully utilized because of either hardware restrictions or the lack of adequate algorithms.
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Block SSOR preconditionings for high order 3D FE systems
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On Numerical Solution of the Markov Renewal Equation: Tight Upper and Lower Kernel Bounds
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TL;DR: The authors' algorithm and computed bounds are used to study the expected number of departures as a function of time for a two node overflow queueing network and Computational error and numerical stability for computing the bounds in parallel are discussed.
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References
•Book
The Theory of Matrices in Numerical Analysis
Alston S. Householder
- 01 Jan 1964
TL;DR: A wall-mounted oil clarification system for use in clarifying oil in a deep fat fryer disposed below the system.
1.6K
Access and Alignment of Data in an Array Processor
TL;DR: This paper discusses the design of a primary memory system for an array processor which allows parallel, conflict-free access to various slices of data, and subsequent alignment of these data for processing, and a network based on Stone's shuffle-exchange operation is presented.
1.2K
Time and Parallel Processor Bounds for Linear Recurrence Systems
Shyh-Ching Chen,D.J. Kuck +1 more
TL;DR: By a simple transformation, the results can also be applied to the solution of any triangular linear system of equations Ax̄ = b̄, and the computer need only perform one type of operation at each time step.
100
Solving Triangular Systems on a Parallel Computer
Ahmed H. Sameh,Richard P. Brent +1 more
TL;DR: In this paper, alternative formulations of the algorithms of Chen and Kuck are presented and a detailed error analysis is given, showing that if $\tilde x$ is the computable number, then Chen-Kuck algorithms are invalid.
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