El Mostafa Daoudi

Optimal algorithms for parallel Givens factorization on a coarse-grained PRAM

We study the complexity of the parallel Givens factorization of a square matrix of size n on a shared memory architecture composed with p identical processors (coarse grained EREW PRAM). We show how to construct an asymptotically optimal algorithm. We deduce that tje time complexity is equal to: ... (formule)... and that the minimum number of processors in order to compute the Givens factorization in asymptotically optimal time (2n + o(n)) is equal to p opt = n/(2 + √2) + o(n). These results complete previous analysis presented in the case where the number of processors is unlimited

Implementation of a boundary element method on distributed memory computers

Abstract In this paper, we analyse and compare different parallel implementations of the Boundary Element Method on distributed memory computers. We deal with the computation of two-dimensional magnetostatic problems. The resulting linear system will be solved using Householder transformation and Gaussian elimination. Experimental results are obtained on a Meiko Computing Surface with 32 T800 transputers.

Parallelization of the Continuous Global Optimization Problem with Inequality Constraints by Using Interval Arithmetic

In this work, we study on distributed memory architecture, the parallelization of the continuous global optimization problem, based on interval arithmetic, with inequality constraints. Since this algorithm is dynamic and irregular, we propose, in particular, some techniques taking into account the load balancing problem.

Parallel Methods of Training for Multilayer Neural Network

In this paper, we present two parallel techniques of training for multilayer neural network. One technique is based on the duplication of the network but the other one is based on the distribution of the multilayer network onto processors. We only have implemented the first parallel technique under PVM, but the parallel implementations for the second one are in progress.

Exploiting the symmetry in the parallelization of the Jacobi method

Abstract In this paper, we propose a new parallel algorithm which exploits the symmetry of the Jacobi method for computing the eigenvalues of a real and symmetric square matrix A on a distributed memory multiprocessor.

Study of the Parallel Block One-Sided Jacobi Method

In this paper, we study the parallelization of the one-sided Jacobi method for computing the eigenvalues and the eigenvectors of a real and symmetric matrix. We use a technique to overlap the communications by the computations in order to decrease the global communication time. We also extend the obtained results to the block version for using the level-3 BLAS.

Parallel Givens Factorization on a Shared Memory Multiprocessor

The complexity of parallel Givens factorization on a shared memory architecture composed with p identical processors has been determined for square matrices [6]. For the rectangular case the problem of the optimality (construction and execution time of the optimal algorithm) is still open. In this paper we describe two parallel algorithms to compute the Givens factorization of a rectangular matrix of size mxn (m ≥ n). The first one is formulated for any m, n and p. Its execution time is equal to (mn-n(n+1)/2)/p +3p/2 + o (p). The second one is for p ≤ min(m/4, n/2). Its execution time is equal to (mn-n(n+1)/2)/p + p/2 + o(p) if m-n > p, and (mn-n(n+1)/2)/p + p + (m-n)(m-n-2p)/2p + o(p) if m-n ≤ p. We think that the second algorithm is asymptotically optimal and prove it for m=n.

Parallelization of Image Compression on Distributed Memory Architecture

In this work we propose two parallel algorithms, for image compression, based on multilayer neural networks, by subdividing the image into blocks. The first parallel technique is based on a static distribution of blocks to processors. The advantage of this distribution is that the training phase (construction of the compressor-decompressor network) does not need any communication but its drawback is the load balancing problem. The second parallel technique improves the load balancing problem by using a dynamic distribution of blocks but it requires communication between processors. These two implementations are tested and compared on a distributed memory machine under PVM.

Parallel electromagnetic modelling for the nonlinear electrotechnic systems

We present a parallel implementation for the nonlinear electromagnetic modelling using PVM environment. Theoretical study shows that the computation can be highly parallelizable but the communication can be a handicap if we do not overlap communication with computation especially when the machine communication parameters values are very high.

Overlapping Computation/Communication in the Parallel One-Sided Jacobi Method

In this work, we propose some techniques for overlapping the communication by the computation in the parallelization of the one-sided Jacobi method for computing the eigenvalues and the eigenvectors of a real and symmetric matrix. The proposed techniques are experimented on a cluster of PCs and on the parallel system TN310.