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Abstract: The most efficient previously known parallel algorithms for the inversion of a nonsingular n x n matrix .4 or solving a linear system/Ix = b over the rational numbers require O(logn) time and M(n).x/ processors [provided that M(n) processors suffice in order to multiply two n x n rational matrices in time O(log n)]. Furthermore, the known polylog arithmetic time algorithms for those problems are numerically unstable. In this paper we apply Newton's iteration and initially choose an... (Update)
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.... 0) Numerical approximation is involved in this algorithm at the auxiliary stages of matrix inversions, where a parallel algorithm of [PR89] is applied. If A is filled with integers, then this stage can be performed exactly, by using the algorithms of [P85] P87] Then, the...
.... by Reif [29] and by Bini and Pan [1] page 357) Gaussian elimination with no pivoting [2] and Newton s iterative method [24, 25, 27] This selection covers a wide spectrum of features, and is (in some sense) a complete one . Csanky s algorithm, the easiest to describe...
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BibTeX entry: (Update)
V. Y. Pan, J. Reif, Fast and Efficient Parallel Solution of Dense Linear Systems, Compuaters & Mathematics (with Applications), 17, 11, 1481-1491, 1989. http://citeseer.ist.psu.edu/pan89fast.html More
@article{ pan89fast,
author = "Victor Y. Pan and John H. Reif",
title = "Fast and Efficient Solution of Path Algebra Problems",
journal = "Journal of Computer and System Sciences",
volume = "38",
number = "3",
pages = "494-510",
year = "1989",
url = "citeseer.ist.psu.edu/pan89fast.html" }
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