Clusters of computers can be used together to provide a powerful computing resource. Large Monte Carlo simulations, such as those used to model particle growth, are computationally intensive and take considerable time to execute on conventional workstations. By spreading the work of the simulation across a cluster of computers, the elapsed execution time can be greatly reduced. Thus a user has apparently the performance of a supercomputer by using the spare cycles on other workstations.

ABSTRACT We present the parallel implementation on a transputer network of two preconditioned Lanczos-type schemes for the solution of unsymmetric sparse Linear systems: Bi-CGSTAB and TFQMR Solution of a number of sample tests shows that Bi-CGSTAB with ILU preconditioning is generally Faster than TFQMR, but do not achieve. a high degree of parallelize!ion. Better paraLlelization is obtained with the diagonal preconditioner, which uses less memory and allows therefore the solution of larger problems. With this preconditioner the TFQMR algorithm is found to be more robust than Bi-CGSTAB, but not always globally more efficient. The speed Ups obtained with 8 processors in this case reached a maximum of approximately 6.82, showing the high degree of parallelization achievable with the diagonal preconditioner. As in most massively parallel scenarios, however, the attainable speed ups are strongly dependent on the problem granularity.

ABSTRACT We present two new parallel algorithms for exact (error-free) solution of a system of linear equations on a distributed-memory multiprocessor. The exact solution is obtained using the congruence technique which consists of two steps: First, the system of linear equations is converted to systems of linear congruence equations with respect to several prime moduli, and each of these systems is solved on a separate processor. Then, these solutions are combined using the mixed-radix conversion algorithm to obtain the exact solution. The first step is completely (embarrassingly) parallel with no communication requirements among the processors. We improve our previous work and describe two efficient parallel algorithms for the second step. We present the results of our experiments on an Intel iPSC/860 with 8 processors. A linear system of dimension 128 with integer entries as large as 10577 is solved in about 195 seconds on 8 processors with an efficiency of 99.76%.

In this paper, the parallelisation of the stride of three method for the solution of a tridiagonal system of equations for P processors is investigated. The presented algorithm is organised in such a way that all processors are fully operational at every stage of the solution process. The results of experiments carried out on the Sequent Balance 8000 multiprocessor are presented.

We present in this paper the parallelization of fast matrix multiplication algorithms of Strassen and Wino-grad on MIMD distributed architectures whose interconnection networks are ring and torus. Complexity and efficiency are analyzed and good asymptotic behaviour is proved. These new parallel algorithms are compared with standard algorithms on a 128-processor parallel computer; experiments confirm the theoretical results.

ABSTRACT This paper is concerned with the solution of block tridiagonal linear systems by the preconditioned conjugate gradient (PCG) method. If we consider a block AGE splitting of the coefficient matrix, it is possible to derive an additive polynomial preconditioner and to give conditions for such preconditioner to be symmetric positive definite. Numerical experiments on diffusion problem are carried out on Cray Y-MP in order to evaluate the effectiveness of the parallel polynomial preconditioner.

Our work is concerned with the derivation of systolic arrays for certain Toeplitz linear systems of equations. First, the notion of Toeplitz systems is presented. Then, the solution of tridiagonal systems of equations is discussed. It is based on a QQT factorisation, where Q is an upper bidiagonal rectangular Toeplitz matrix. Next, the algorithm for solving a tridiagonal system of equations is analysed. The single assignment code algorithms arc derived and the broadcast of data is removed. The data dependence method is used for mapping algorithms into systolic arrays.

ABSTRACT In this work PFI (Perturbed Functional Iterations) has been extended to solve large-scale nonlinear models by applying parallel computations. PFI partially linearizes a given nonlinear system, and irrespective of the physical dimension of the model it solves in parallel a sequence of linear equations of significantly smaller order to compute perturbation parameters and adds them in parallel to nonlinear Jacobi iterations to compute new iterates. As convergence is approached all linearizations are damped out, restoring thereby nonlinear properties of the model near the root. This generates a high degree of accuracy. In comparison with other nonlinear algorithms, PFI has a simple algorithm which is easy to program. Some applications have produced encouraging results.

In this paper we present an integrated model for decomposition and mapping (D&M) of Locally Connected Layered Neural Networks (LCLNs) on message-passing multiprocessors. Within the framework of this model we analyze two previously proposed D&M strategies for a particular class of LCLNs. The model is compared with the performance of a neural network simulation environment, running on a transputer array. We find that both strategies may be applicable, depending on the network size, and we can determine the problem size at which one strategy is preferred over the other. Furthermore, we find that the regularity of the communication pattern between the processors is an unexpected factor in the D&M decision.