An hybrid parallel algorithm for solving tridiagonal linear systems versus the Wang’s method in a Cray T3D BSP computer

In this paper we describe an hybrid algorithm for an even number of processors based on an algorithm for two processors and the Overlapping Partition Method for tridiagonal systems. Moreover, we compare this hybrid method with the Partition Wang’s method in a BSP computer. Finally, we compare the theoretical computation cost of both methods for a Cray T3D computer, using the cost model that BSP model provides.

Sequential and parallel synchronous alternating iterative methods

The so-called parallel multisplitting nonstationary iterative Model A was introduced by Bru, Elsner, and Neumann [Linear Algebra and its Applications 103:175-192 (1988)] for solving a nonsingular linear system Ax = b using a weak nonnegative multisplitting of the first type. In this paper new results are introduced when A is a monotone matrix using a weak nonnegative multisplitting of the second type and when A is a symmetric positive definite matrix using a P -regular multisplitting. Also, nonstationary alternating iterative methods are studied. Finally, combining Model A and alternating iterative methods, two new models of parallel multisplitting nonstationary iterations are introduced. When matrix A is monotone and the multisplittings are weak nonnegative of the first or of the second type, both models lead to convergent schemes. Also, when matrix A is symmetric positive definite and the multisplittings are P -regular, the schemes are also convergent.

Parallel relaxed and extrapolated algorithms for computing PageRank

In this paper, parallel Relaxed and Extrapolated algorithms based on the Power method for accelerating the PageRank computation are presented. Different parallel implementations of the Power method and the proposed variants are analyzed using different data distribution strategies. The reported experiments show the behavior and effectiveness of the designed algorithms for realistic test data using either OpenMP, MPI or an hybrid OpenMP/MPI approach to exploit the benefits of shared memory inside the nodes of current SMP supercomputers.