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Mathematics of Computation

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Euclid’s algorithm and the Lanczos method over finite fields

Author: Jeremy Teitelbaum
Journal: Math. Comp. 67 (1998), 1665-1678
MSC (1991): Primary 11Y16, 65F10, 15A33
MathSciNet review: 1474657
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Abstract: This paper shows that there is a close relationship between the Euclidean algorithm for polynomials and the Lanczos method for solving sparse linear systems, especially when working over finite fields. It uses this relationship to account rigorously for the appearance of self-orthogonal vectors arising in the course of the Lanczos algorithm. It presents an improved Lanczos method which overcomes problems with self-orthogonality and compares this improved algorithm with the Euclidean algorithm.

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Jeremy Teitelbaum
Affiliation: Jeremy Teitelbaum, Department of Mathematics, Statistics, and Computer Science (M/C 249), University of Illinois at Chicago, 851 S. Morgan St., Chicago, IL 60607, USA

Received by editor(s): February 8, 1996
Additional Notes: The author is supported by the National Science Foundation.
Article copyright: © Copyright 1998 American Mathematical Society