Journal Article10.1016/0167-8191(89)90119-1
A fast vector algorithm for solving tridiagonal linear equations
M Bessendrodt-Weberpals,H Weberpals +1 more
- 01 Feb 1989
- Vol. 9, Iss: 3, pp 367-372
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TL;DR: A fast vector algorithm which solves tridiagonal linear equations by an optimum synthesis of the inherently recursive Gaussian elimination and the parallel though complex cyclic reduction and a maximum vector speedup of 13 is revealed.
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Abstract: We present a fast vector algorithm which solves tridiagonal linear equations by an optimum synthesis of the inherently recursive Gaussian elimination and the parallel though complex cyclic reduction. The idea is to perform an incomplete cyclic reduction to bring the dimension of the tridiagonal system efficiently below a characteristic size n ∗ and then to solve the remaining system by Gaussian elimination. Extensive numerical experiments on the CYBER 205 and the CRAY X-MP computers reveal a maximum vector speedup of 13 and prove n ∗ to reflect the architecture of the vector computer. The performance is further enhanced when a feq right-hand sides are treated simultaneously.
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Citations
On the parallel solution of tridiagonal systems by wrap-around partitioning and incomplete LU factorization
TL;DR: Two methods are presented which efficiently solve tridiagonal systems on vector supercomputers and parallel computers with a moderate degree of parallelism based on wrap-around partitioning, which is closely related to the partitioning used in Wang's algorithm.
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Unified framework for the parallelization of divide and conquer based tridiagonal systems
Juan Antonio Sánchez López,Oscar Plata,Francisco Argüello,Emilio L. Zapata,Emilio L. Zapata +4 more
- 29 Jun 1997
TL;DR: A method for the regularization and parallelization of tridiagonal algorithms based on the divide and conquer strategy based on perfect shuffle and unshuffle permutations which transform the flow of these algorithms into a flow with the same pattern of communications in all the stages.
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Cyclic reduction for tridiagonal systems of equations with interval coefficients on vector computers
TL;DR: Nterval arithmetic versions of cyclic reduction algorithms are introduced for tridiagonal systems of equations with interval coefficients on vector computers to replace the recursive Gauss algorithm by a method with some parallelism.
10
Architectural approach to the IBM 3090E vector performance
Helmut Weberpals
- 01 Jan 1990
TL;DR: The architecture of the vector facility and the three-level memory hierarchy is reviewed, timing formulae for the basic arithmetic, load, and store instructions are derived, and the influence of the cache design is pinpointed.
7
Improving the vector performance via algorithmic domain decomposition
Helmut Weberpals
- 01 Sep 1990
TL;DR: This work uses the IBM 3090 as a paradigm and gives a fairly complete account of its cache storage which turns out to play a crucial role in vector processing.
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