Efficient parallel solution of linear systems
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
Complexity of parallel matrix computations
Theoretical Computer Science
Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Polynomial and matrix computations (vol. 1): fundamental algorithms
Polynomial and matrix computations (vol. 1): fundamental algorithms
Parallel Matrix Multiplication on a Linear Array with a Reconfigurable Pipelined Bus System
IEEE Transactions on Computers
IPDPS '01 Proceedings of the 15th International Parallel & Distributed Processing Symposium
| Hi-index | 0.00 |
We present fast and scalable parallel computations for a number of important and fundamental matrix problems on distributed memory systems (DMS). These problems include computing the powers, the inverse, the characteristic polynomial, the determinant, the rank, the Krylov matrix, and an LU- and a QR-factorization of a matrix, and solving linear systems of equations. These parallel computations are based on efficient implementations of the fastest sequential matrix multiplication algorithm on DMS. We show that compared with the best known time complexities on PRAM, our parallel matrix computations achieve the same speeds on distributed memory parallel computers (DMPC), and have an extra polylog factor in the time complexities on DMS with hypercubic networks. Furthermore, our parallel matrix computations are fully scalable on DMPC and highly scalable over a wide range of system size on DMS with hypercubic networks. Such fast and scalable parallel matrix computations were not seen before on any distributed memory systems.