Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Asymptotically fast computation of Hermite normal forms of integer matrices
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Triangular x-basis decompositions and derandomization of linear algebra algorithms over K[x]
Journal of Symbolic Computation
| Hi-index | 0.00 |
Many linear algebra problems over the ring ZN of integers modulo N can be solved by transforming via elementary row operations an n × m input matrix A to Howell form H. The nonzero rows of H give a canonical set of generators for the submodule of (ZN)m generated by the rows of A. In this paper we present an algorithm to recover H together with an invertible transformation matrix P which satisfies PA = H. The cost of the algorithm is O(nmω-1) operations with integers bounded in magnitude by N. This leads directly to fast algorithms for tasks involving ZN-modules, including an O(nmω-1) algorithm for computing the general solution over ZN of the system of linear equations xA = b, where b ∈ (ZN)m.