Fraction-free algorithms for linear and polynomial equations

Authors:
George C. Nakos;Peter R. Turner;Robert M. Williams
Affiliations:
Mathematics Department, US Naval Academy, Annapolis, MD;Mathematics Department, US Naval Academy, Annapolis, MD;Naval Air Warfare Center Aircraft Division, Patuxent River Naval Air Station, MD
Venue:
ACM SIGSAM Bulletin
Year:
1997

Citing 0
Cited 3

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Abstract

This paper extends the ideas behind Bareiss's fraction-free Gauss elimination algorithm in a number of directions. First, in the realm of linear algebra, algorithms are presented for fraction-free LU "factorization" of a matrix and for fraction-free algorithms for both forward and back substitution. These algorithms are valid not just for integer computation but also for any matrix system where the entries are taken from a unique factorization domain such as a polynomial ring. The second part of the paper introduces the application of the fraction-free formulation to resultant algorithms for solving systems of polynomial equations. In particular, the use of fraction-free polynomial arithmetic and triangularization algorithms in computing the Dixon resultant of a polynomial system is discussed.