M. Giesbrecht, Efficient parallel solution of sparse systems of linear diophantine equations, in: Second International Symposium on Parallel Symbolic Computation (PASCO'97), Maui, HI, USA, July 1997, pp. 1--10.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....in order to avoid too high a slowdown of the matrix vector product for the resulting preconditioned matrix. Our target problems discussed are linear system solution, determinant, and rank. Solutions to additional problems such as Diophantine problems (over the integers) and Smith form computation [7,8,17] also involve these preconditioners. Future work may concern the use of preconditioners to compute the characteristic polynomial of a matrix and matrix normal forms, as well as conditioners to preserve additional structural properties. L. Chen et al. Linear Algebra and its Applications ....

M. Giesbrecht, Efficient parallel solution of sparse systems of linear diophantine equations, in: Second International Symposium on Parallel Symbolic Computation (PASCO'97), Maui, HI, USA, July 1997, pp. 1--10.

....Proceedings of ISSAC 99: ACM International Symposium on Symbolic and Algebraic Computation, July 1999, Vancouver, Canada. log fi small compared to n, this improves on the previously fastest algorithm which uses O Gamma n 4 log fi nM(n log fi) Delta bit operations in the worst case [7]. Moreover, the algorithm we present here, like that in [7] requires additional storage for only O Gamma n 2 (log n log fi) Delta bits. This space complexity, which is linear in the size of the output vector and essentially linear in the size of a dense input system, is an important ....

....on Symbolic and Algebraic Computation, July 1999, Vancouver, Canada. log fi small compared to n, this improves on the previously fastest algorithm which uses O Gamma n 4 log fi nM(n log fi) Delta bit operations in the worst case [7] Moreover, the algorithm we present here, like that in [7], requires additional storage for only O Gamma n 2 (log n log fi) Delta bits. This space complexity, which is linear in the size of the output vector and essentially linear in the size of a dense input system, is an important feature of the algorithm. The global technique of our ....

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M. Giesbrecht. Efficient parallel solution of sparse systems of linear diophantine equations. In M. Hitz and E. Kaltofen, editors, Second Int'l Symp. on Parallel Symbolic Computation: PASCO '97, pages 1--10. ACM Press, 1997.

.... Inconsistency of Sparse Linear Systems M. Giesbrecht Dept. of Computer Science University of Manitoba Winnipeg, Manitoba R3T 2N2, Canada email: mwg cs.umanitoba.ca A. Lobo Dept. of Mathematics and Computer Science Washington College, 300 Washington Ave. Chestertown, MD, 21620, USA Email: Austin.Lobo washcoll.edu B. D. Saunders y Dept. of ....

.... probabilistic algorithms which exploit sparsity in A have been developed to solve the problem of finding solutions x if one exists (over fields by Wiedemann 1986, Kaltofen Saunders 1991, Coppersmith 1993, Coppersmith 1994, Kaltofen 1995, Lambert 1996, Villard 1997, and over the integers by Giesbrecht 1997). Furthermore a purported solution is easily checked, so that these algorithms are of Las Vegas type when the hypothesis is made a priori that the system is consistent. However, less attention has been paid to the case when no solutions exists, and these algorithms do not certify this case. There ....

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M. Giesbrecht. Efficient parallel solution of sparse systems of linear diophantine equations. In Proceediings of PASCO'97, 1997. To appear. 10pp.

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