Deterministic Processor Scheduling
ACM Computing Surveys (CSUR)
A case study in programming for parallel-processors
Communications of the ACM
The solution of linear systems of equations on a vector computer.
The solution of linear systems of equations on a vector computer.
Iterative Solution of Linear Equations on a Parallel Processor System
IEEE Transactions on Computers
Optimal Scheduling Strategies in a Multiprocessor System
IEEE Transactions on Computers
Bounds on the Number of Processors and Time for Multiprocessor Optimal Schedules
IEEE Transactions on Computers
Improving the computation of lower bounds for optimal schedules
IBM Journal of Research and Development
A Data Structure for Parallel L/U Decomposition
IEEE Transactions on Computers
An Efficient Parallel Algorithm for the Solution of Large Sparse Linear Matrix Equations
IEEE Transactions on Computers
Optimal Parallel Scheduling of Gaussian Elimination DAG's
IEEE Transactions on Computers
| Hi-index | 14.99 |
The solution process of Ax = b is modeled by an acyclic directed graph in which the nodes represent the arithmetic operations applied to the elements of A, and the arcs represent the precedence relations that exist among the operations in the solution process. Operations that can be done in parallel are identified in the model and the absolute minimum completion time and lower bounds on the minimum number of processors required to solve the equations in minimal time can be found from it. Properties of the model are derived. Hu's level scheduling strategy is applied to examples of sparse matrix equations with surprisingly good results. Speed-up using parallel processing is found to be proportional to the number of processors when it is 10-20 percent of the order of A.