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Mathematics of Computation

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A parallel algorithm for solving general tridiagonal equations


Author: Paul N. Swarztrauber
Journal: Math. Comp. 33 (1979), 185-199
MSC: Primary 65F05; Secondary 68C25
DOI: https://doi.org/10.1090/S0025-5718-1979-0514818-5
MathSciNet review: 514818
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Abstract: A parallel algorithm for the solution of the general tridiagonal system is presented. The method is based on an efficient implementation of Cramer's rule, in which the only divisions are by the determinant of the matrix. Therefore, the algorithm is defined without pivoting for any nonsingular system. $ O(n)$ storage is required for n equations and $ O(\log n)$ operations are required on a parallel computer with n processors. $ O(n)$ operations are required on a sequential computer. Experimental results are presented from both the CDC 7600 and CRAY-1 computers.


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DOI: https://doi.org/10.1090/S0025-5718-1979-0514818-5
Keywords: Tridiagonal matrices, parallel algorithms, linear equations
Article copyright: © Copyright 1979 American Mathematical Society