Fast parallel computation of the Smith normal form of polynomial matrices
ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
Efficient decomposition of associative algebras
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
Computing Popov and Hermite forms of polynomial matrices
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
Efficient parallel solution of sparse systems of linear diophantine equations
PASCO '97 Proceedings of the second international symposium on Parallel symbolic computation
NC2 computation of gcd-free basis and application to parallel algebraic numbers computation
PASCO '97 Proceedings of the second international symposium on Parallel symbolic computation
Processor-efficient parallel matrix inversion over abstract fields: two extensions
PASCO '97 Proceedings of the second international symposium on Parallel symbolic computation
An O(n3) algorithm for the Frobenius normal form
ISSAC '98 Proceedings of the 1998 international symposium on Symbolic and algebraic computation
Black box Frobenius decompositions over small fields
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
Computing rational forms of integer matrices
Journal of Symbolic Computation
Computer algebra handbook
Efficient decomposition of separable algebras
Journal of Symbolic Computation
On matrix perturbations with minimal leading Jordan structure
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the international conference on linear algebra and arithmetic, Rabat, Morocco, 28-31 May 2001
Processor efficient parallel matching
Proceedings of the seventeenth annual ACM symposium on Parallelism in algorithms and architectures
The shifted number system for fast linear algebra on integer matrices
Journal of Complexity - Festschrift for the 70th birthday of Arnold Schönhage
Faster algorithms for the characteristic polynomial
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Computation of homology groups and generators
Computers and Graphics
The shifted number system for fast linear algebra on integer matrices
Journal of Complexity - Festschrift for the 70th birthday of Arnold Schönhage
Composition collisions and projective polynomials: statement of results
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Algebraic and numerical algorithms
Algorithms and theory of computation handbook
Dynamic normal forms and dynamic characteristic polynomial
Theoretical Computer Science
Computation of homology groups and generators
DGCI'05 Proceedings of the 12th international conference on Discrete Geometry for Computer Imagery
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A Las-Vegas-type probabilistic algorithm is presented for finding the Frobenius canonical form of an $n\times n$ matrix $T$ over any field $\KK$. The algorithm requires $\softO(\MM(n))=\MM(n)\cdot(\log n)^{O(1)}$ operations in $\KK$, where $O(\MM(n))$ operations in $\KK$ are sufficient to multiply two $n\times n$ matrices over $\KK$. This nearly matches the lower bound of $\Omega(\MM(n))$ operations in $\KK$ for this problem, and improves on the $O(n^4)$ operations in $\KK$ required by the previously best known algorithms.A fast parallel implementation of the algorithm is also demonstrated for the Frobenius form, which is processor-efficient on a PRAM. As an application we give an algorithm to evaluate a polynomial $g\in\KK[x]$ at $T$ which requires only $\softO(\MM(n))$ operations in $\KK$ when $\deg g\leq n^2$. Other applications include sequential and parallel algorithms for computing the minimal and characteristic polynomials of a matrix, the rational Jordan form of a matrix (for testing whether two matrices are similar), and for matrix powering which are substantially faster than those previously known.