Generalized multisplitting asynchronous iteration

Parallel , Synchronous and Asynchronous Two - Stage Multisplitting

Different types of synchronous and asynchronous two-stage multisplitting algorithms for the solution of linear systems are analyzed. The different algorithms which appeared in the literature are reviewed, and new ones are presented. Convergence properties of these algorithms are studied when the matrix in question is either monotone or an H-matrix. Relaxed versions of these algorithms are also ...

Modulus-based synchronous multisplitting iteration methods for linear complementarity problems

To reduce the communication among processors and improve the computing time for solving linear complementarity problems, we present a two-step modulus-based synchronous multisplitting iteration method and the corresponding symmetric modulus-based multisplitting relaxation methods. The convergence theorems are established when the system matrix is an H+-matrix, which improve the existing converg...

Solving Large Sparse Linear Systems using Asynchronous Multisplitting

Iterative methods for solving large sparse systems of linear equations are widely used in many HPC applications. Extreme scaling of these methods can be difficult, however, since global communication to form dot products is typically required at every iteration. To try to overcome this limitation we propose a hybrid approach, where the matrix is partitioned into blocks. Within each block, we us...

Multilevel Asynchronous Iteration for PDEs

Numerical Performance of an Asynchronous Jacobi Iteration

We examine the eeect of removing synchronisation points from a parallel implementation of a simple iterative algorithm|Jacobi's method for linear systems. We nd that in some cases the asynchronous version requires fewer iterations to converge than its synchronous counterpart. We show that this behaviour can be explained in terms of the presence or absence of oscillations in the sequence of erro...