For large-scale sparse saddle point problems, Peng and Li [12] have recently proposed a new alternating-direction iterative method for solving nonsingular saddle point problems, which is more competitive (in terms of iteration steps and CPU time) than some classical iterative methods such as Uzawa-type and HSS (Hermitian skew splitting) methods. In this paper, we further study this method when ...

The rate of convergence of the Generalized Minimum Residual Method (GMRES) applied to the dense linear systems arising from discretization of EFIE integral equation by Method of Moment (MoM) depends heavily by preconditioning. In this work, we evaluate the performances of a simple preconditioner based on the skew hermitian component S of MoM impedance matrix Z for the case of plane wave scatter...

In the case of a linear constant coefficient differential equation, & = Ax, where x is a (complex) n-vector and A is a (complex) nXn matrix, it is well known when all solutions are bounded; namely, if all eigenvalues of A are purely imaginary and all elementary divisions of A are simple. This condition is equivalent to the Jordan normal form, / , of A being (Hermitian) skew symmetric. That is i...

We say that a square complex matrix is condensable if it can be reduced to a bandform through a nite sequence of elementary uni-tary similarities. The two main results of this paper are the following assertions: (1) Any matrix with a low rank skew-Hermitian part is condens-able. (2) If A is a normal condensable matrix, then any rank one perturbation of A (generally nonnormal) is condensable as ...

We study the structured distance to singularity for a given regular matrix pencil $A+sE$, where $(A,E)\in \mathbb S \subseteq (\mathbb C^{n,n})^2$. This includes Hermitian, skew-Hermitian, $*$-even, $*$-odd, $*$-palindromic, T-palindromic, and dissipative Hamiltonian pencils. present purely linear algebra-based approach derive explicit computable formulas nearest $(A-\Delta_A)+s(E-\Delta_E)$ su...