4,718 research outputs found
Alternating-Direction Line-Relaxation Methods on Multicomputers
We study the multicom.puter performance of a three-dimensional Navier–Stokes solver based on alternating-direction line-relaxation methods. We compare several multicomputer implementations, each of which combines a particular line-relaxation method and a particular distributed block-tridiagonal solver. In our experiments, the problem size was determined by resolution requirements of the application. As a result, the granularity of the computations of our study is finer than is customary in the performance analysis of concurrent block-tridiagonal solvers. Our best results were obtained with a modified half-Gauss–Seidel line-relaxation method implemented by means of a new iterative block-tridiagonal solver that is developed here. Most computations were performed on the Intel Touchstone Delta, but we also used the Intel Paragon XP/S, the Parsytec SC-256, and the Fujitsu S-600 for comparison
Convergence on Gauss-Seidel iterative methods for linear systems with general H-matrices
It is well known that as a famous type of iterative methods in numerical
linear algebra, Gauss-Seidel iterative methods are convergent for linear
systems with strictly or irreducibly diagonally dominant matrices, invertible
matrices (generalized strictly diagonally dominant matrices) and Hermitian
positive definite matrices. But, the same is not necessarily true for linear
systems with nonstrictly diagonally dominant matrices and general matrices.
This paper firstly proposes some necessary and sufficient conditions for
convergence on Gauss-Seidel iterative methods to establish several new
theoretical results on linear systems with nonstrictly diagonally dominant
matrices and general matrices. Then, the convergence results on
preconditioned Gauss-Seidel (PGS) iterative methods for general matrices
are presented. Finally, some numerical examples are given to demonstrate the
results obtained in this paper
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