Acceleration of Euclidean algorithm and extensions

Authors:
Victor Y. Pan;Xinmao Wang
Affiliations:
Lehman College of CUNY, Bronx, NY;Graduate School of CUNY, New York, NY
Venue:
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Year:
2002

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Abstract

We accelerate the extended Euclidean algorithm for integers, the rational number reconstruction, and consequently, the stage of the recovery of the solution of a nonsingular integer system of linear equations via Hensel's lifting. The acceleration is by the order of magnitude and yields nearly optimal randomized algorithms. In the highly important case of Toeplitz, Hankel, and Toeplitz/Hankel-like linear systems, the accleration is potentially practical.