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Efficient Tridiagonal Solvers on Multicomputers
March 1992 (vol. 41 no. 3)
pp. 286-296

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.

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Index Terms:
parallel partition LU algorithm; computation complexity; tridiagonal solvers; multicomputers; parallel algorithms; parallel partition hybrid; parallel diagonal dominant; tridiagonal linear systems; divide-and-conquer parallel computation model; pivoting; nonpivoting; approximate solution; communication complexities; 64-node nCUBE-1 multicomputer; computational complexity; linear algebra; mathematics computing.
X.-H. Sun, H. Zhang, L.M. Ni, "Efficient Tridiagonal Solvers on Multicomputers," IEEE Transactions on Computers, vol. 41, no. 3, pp. 286-296, March 1992, doi:10.1109/12.127441
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