18 research outputs found
Accelerated generalized SOR method for a class of complex systems of linear equations
For solving a broad class of complex symmetric linear systems, recently Salkuyeh et al. recast the system in a real formulation and studied a generalized successive overrelaxation (GSOR) iterative method. In this paper, we introduce an accelerated GSOR (AGSOR) iterative method which involves two iteration parameters. Then, we theoretically study its convergence properties and determine its optimal iteration parameters and corresponding optimal convergence factor. Finally, some numerical computations are presented to validate the theoretical results and compare the performance of the AGSOR method with those of the GSOR and MHSS methods
A variant of the AOR method for augmented systems
A variant of the AOR method for augmented system
Quasi-Perron-Frobenius property of a class of saddle point matrices
The saddle point matrices arising from many scientific computing fields have
block structure , where the sub-block is symmetric and positive definite, and
is symmetric and semi-nonnegative definite. In this article we report a
unobtrusive but potentially theoretically valuable conclusion that under some
conditions, especially when is a zero matrix, the spectral radius of
must be the maximum eigenvalue of . This characterization approximates to
the famous Perron-Frobenius property, and is called quasi-Perron-Frobenius
property in this paper. In numerical tests we observe the saddle point matrices
derived from some mixed finite element methods for computing the stationary
Stokes equation. The numerical results confirm the theoretical analysis, and
also indicate that the assumed condition to make the saddle point matrices
possess quasi-Perron-Frobenius property is only sufficient rather than
necessary