We construct, analyze and implement SSOR-like preconditioners for non-Hermitian positive definite system of linear equations when its coefficient matrix possesses either a dominant Hermitian part or a dominant skew-Hermitian part. We derive tight bounds for eigenvalues of the preconditioned matrices and obtain convergence rates of the corresponding SSOR-like iteration methods as well as the cor...

We construct, analyze and implement SSOR-like preconditioners for non-Hermitian positive definite system of linear equations when its coefficient matrix possesses either a dominant Hermitian part or a dominant skew-Hermitian part. We derive tight bounds for eigenvalues of the preconditioned matrices and obtain convergence rates of the corresponding SSOR-like iteration methods as well as the cor...

It is known that the Hermitian and skew-Hermitian splitting (HSS) iteration method is an efficient solver for non-Hermitian positive definite linear system of equations. In [M. Benzi, SIAM J. Matrix Anal. Appl. 31 (2009) 360–374] Benzi proposed a generalization of the HSS (GHSS) iteration method. In this paper, we present a two-parameter version of the GHSS (TGHSS) method and investigate its co...

We study solutions of almost periodic linear differential systems. This field is called the Favard theory what is based on the famous Favard result in [10] (see, e.g., [3, Theorem 1.2] or [28, Theorem 1]). It is a well-known corollary of the Favard (and the Floquet) theory that any bounded solution of a periodic linear differential system is almost periodic (see [12, Corollary 6.5] and [13] for...

We generalize the accelerated Hermitian and skew-Hermitian splitting (AHSS) iteration methods for large sparse saddle-point problems. These methods involve four iteration parameters whose special choices can recover the preconditioned HSS and accelerated HSS iteration methods. Also a new efficient case is introduced and we theoretically prove that this new method converges to the unique solutio...

We study the preconditioned iterative method for the unsteady Navier-Stokes equations. The rotation form of the Oseen system is considered. We apply an efficient preconditioner which is derived from the Hermitian/Skew-Hermitian preconditioner to the Krylov subspace-iterative method. Numerical experiments show the robustness of the preconditioned iterative methods with respect to the mesh size, ...