Algorithms for the solution of systems of linear equations in commutative ring
Symbolic Computation
2017-12-01 v1
Abstract
Solution methods for linear equation systems in a commutative ring are discussed. Four methods are compared, in the setting of several different rings: Dodgson's method [1], Bareiss's method [2] and two methods of the author - method by forward and back-up procedures [3] and a one-pass method [4]. We show that for the number of coefficient operations, or for the number of operations in the finite rings, or for modular computation in the polynomial rings the one-pass method [4] is the best. The method of forward and back-up procedures [3] is the best for the polynomial rings when we make use of classical algorithms for polynomial operations.
Cite
@article{arxiv.1711.11471,
title = {Algorithms for the solution of systems of linear equations in commutative ring},
author = {Gennadi Malaschonok},
journal= {arXiv preprint arXiv:1711.11471},
year = {2017}
}
Comments
10 pages. arXiv admin note: substantial text overlap with arXiv:1711.11472