Abstract
An error complexity analysis of two algorithms for solving a unit diagonal triangular system is given. The results show that the usual sequential algorithm is optimal in terms of having the minimal maximum and cumulative error complexity measures. The parallel algorithm described by Sameh and Brent is shown to be essentially equivalent to the optimal sequential one.
This work was supported in part by an ASEE-NASA 1988 Summer Faculty Fellowship and in part by NASA while the author was visiting ICOMP, NASA Research Center, Cleveland, Ohio.
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References
A. H. Sameh and R. P. Brent, Solving triangular systems on a parallel computer, SIAM J. Numer. Anal., 14 (1977), pp. 1101–1113.
J. H. Wilkinson, Rounding Errors in Algebraic Processes, Prentice-Hall, Englewood Cliffs, NJ, 1963.
N. K. Tsao, Solving triangular systems in parallel is not bad, submitted for publication.
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© 1991 Springer-Verlag Berlin Heidelberg
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Tsao, Nk. (1991). Solving Triangular System in Parallel is Accurate. In: Golub, G.H., Van Dooren, P. (eds) Numerical Linear Algebra, Digital Signal Processing and Parallel Algorithms. NATO ASI Series, vol 70. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-75536-1_51
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DOI: https://doi.org/10.1007/978-3-642-75536-1_51
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