On computing determinants of matrices without divisions
ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
Algorithmic number theory
Diophantine linear system solving
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
Fast deterministic computation of determinants of dense matrices
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
On computing the determinant and Smith form of an integer matrix
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Computing the sign or the value of the determinant of an integer matrix, a complexity survey
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the international conference on linear algebra and arithmetic, Rabat, Morocco, 28-31 May 2001
Smith normal form of dense integer matrices fast algorithms into practice
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
On the complexity of computing determinants
Computational Complexity
A BLAS based C library for exact linear algebra on integer matrices
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Computing the smith forms of integer matrices and solving related problems
Computing the smith forms of integer matrices and solving related problems
Efficient parallelizations of Hermite and Smith normal form algorithms
Parallel Computing
The shifted number system for fast linear algebra on integer matrices
Journal of Complexity - Festschrift for the 70th birthday of Arnold Schönhage
Deterministic unimodularity certification
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
| Hi-index | 0.00 |
We present a new heuristic algorithm for computing the determinant of a nonsingular n x n integer matrix. Extensive empirical results from a highly optimized implementation show the running time grows approximately as n3 log n, even for input matrices with a highly nontrivial Smith invariant structure. We extend the algorithm to compute the Hermite form of the input matrix. Both the determinant and Hermite form algorithm certify correctness of the computed results.