Parallel Elimination Method Research Articles

Region analysis: a parallel elimination method for data flow analysis

Parallel data flow analysis methods offer the promise of calculating detailed semantic information about a program at compile-time more efficiently than sequential techniques. Previous work on parallel elimination methods (Zobel, 1990) has been hampered by the lack of control over interval size; this can prohibit effective parallel execution of these methods. To overcome this problem, we have designed the region analysis method, a new elimination method for data flow analysis. Region analysis emphasizes flow graph partitioning to enable better load balancing in a more effective parallel algorithm. We present the design of region analysis and the empirical results we have obtained that indicate: the prevalence of large intervals in flow graphs derived from real programs; and the performance improvement of region analysis over parallel Allen-Cocke interval analysis. Our implementation analyzed programs from the Perfect Benchmarks and netlib running on a Sequent Symmetry S81. >

A parallel elimination method for the solution of banded linear systems

The algoritm of Chawla et al [1] for tridiagonal linear systems is generalized to obtain a parallel elimination method for the solution of banded linear systems suitable for a multi-processor machine.

A parallel elimination algorithm for the solution of dense linear systems

For the solution of an N × N linear system Ax = d, based on the folding method of Evans and Hatzopoulos [4] and by partitioning the system into r 2 blocks each of size n × n (N = r n), in [3] we had described a parallel elimination method suitable for an r-processor machine. The serial arithmetical operations count for this algorithm is 0(1/3(3 − l/r)N 3) thereby the algorithm could perform with efficiency E r = 2/(3 − 1/r); note that 2/3 ≤ Er ≤ 4/5. In the present paper we consider an alternative elimination procedure together with the method of partitioning to obtain a parallel algorithm for the solution of dense linear systems. The serial arithmetical operations count for the present algorithm is 0(2/3N 3), which is of the same order as that for the standard Gaussian elimination method; thus the present algorithm could perform with efficiency close to 1 on a multiprocessor machine.

A comparison of sequential and parallel elimination methods for tridiagonal matrices

In this paper, parallel forms of the Gaussian and Jordan Elimination schemes for solving the tridiagonal linear systems which occur frequently in Computational Mathematics are developed and compared with the existing sequential algorithms.

Triangularization of a positive definite matrix on a parallel computer

The problem of computing the triangular factors of a square, real, symmetric, and positive definite matrix by using the facilities of a multiprocessor MIMD-type computer is considered. The parallel algorithms based on Cholesky decomposition and Gaussian elimination are derived and analyzed in terms of their speedup and efficiency, when the available number of processors is O( n), where n is the size of the matrix. It is shown that the parallel elimination method can achieve the same speedup as the parallel Cholesky method while using only half the number of processors required by the Cholesky method.