Fast parallel computation of hermite and smith forms of polynomial matrices
SIAM Journal on Algebraic and Discrete Methods
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Asymptotically fast triangularization of matrices over rings
SIAM Journal on Computing
Fast parallel computation of the Smith normal form of polynomial matrices
ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
Fast computation of the Smith normal form of an integer matrix
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
Near optimal algorithms for computing Smith normal forms of integer matrices
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
On the worst-case complexity of integer Gaussian elimination
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Integer matrix diagonalization
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
Algorithm 287: matrix triangulation with integer arithmetic [F1]
Communications of the ACM
An Efficient Algorithm for Out-of-Core Matrix Transposition
IEEE Transactions on Computers
Toward data distribution independent parallel matrix multiplication
IPPS '95 Proceedings of the 9th International Symposium on Parallel Processing
Integer matrices and Abelian groups (invited)
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
Sourcebook of parallel computing
Sourcebook of parallel computing
Parallel Matrix Distribution Library for Sparse Matrix Solvers
HPCASIA '05 Proceedings of the Eighth International Conference on High-Performance Computing in Asia-Pacific Region
Parallel Programming in C with MPI and OpenMP
Parallel Programming in C with MPI and OpenMP
Computing the invariant structure of integer matrices: fast algorithms into practice
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
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Hermite and Smith normal form are important forms of matrices used in linear algebra. These terms have many applications in group theory and number theory. As the entries of the matrix and of its corresponding transformation matrices can explode during the computation, it is a very difficult problem to compute the Hermite and Smith normal form of large dense matrices. The main problems of the computation are the large execution times and the memory requirements which might exceed the memory of one processor. To avoid these problems, we develop parallelizations of Hermite and Smith normal form algorithms. These are the first parallelizations of algorithms for computing the normal forms with corresponding transformation matrices, both over the rings Z and F[x]. We show that our parallel versions have good efficiency, i.e., by doubling the processes, the execution time is nearly halved. Furthermore, they succeed in computing normal forms of dense large example matrices over the rings Q[x], F"3[x], and F"5[x].