Some results concerning hyperinvariant subspaces of some operators on locally convex spaces are considered. Denseness of a class of operators which have a hyperinvariant subspace in the algebra of locally bounded operators is proved.

It is proved that in order to find a nontrivial hyperinvariant subspace for a cohyponormal operator it suffices to make the further assumption that the operator have the single-valued extension property.

The aim of this paper is two-fold. First, we propose an efficient implementation of the continuous time waveform relaxation (WR) method based on block Krylov subspaces. Second, we compare this new WR–Krylov implementation against Krylov subspace methods combined with the shift and invert (SAI) technique. Some analysis and numerical experiments are presented. Since the WR–Krylov and SAI–Krylov m...

The aim of this paper is two-fold. First, we propose an efficient implementation of the continuous time waveform relaxation method based on block Krylov subspaces. Second, we compare this new implementation against Krylov subspace methods combined with the shift and invert technique.

In this paper, we present new variants of global bi-conjugate gradient (Gl-BiCG) and global bi-conjugate residual (Gl-BiCR) methods for solving nonsymmetric linear systems with multiple right-hand sides. These methods are based on global oblique projections of the initial residual onto a matrix Krylov subspace. It is shown that these new algorithms converge faster and more smoothly than the Gl-...

Given the matrices A and E in Cn×n, we consider, for the family A(t) = A+ tE, t ∈ C, questions such as i) existence and analyticity of t 7→ R(t, z) = (A(t) − zI)) , and ii) limit as |t| → ∞ of σ(A(t)), the spectrum of A(t). The answer depends on the Jordan structure of 0 ∈ σ(E), more precisely on the existence of trivial Jordan blocks (of size 1). The results of the theory of Homotopic Deviatio...

Krylov implicit integration factor (IIF) methods were developed in Chen and Zhang (J Comput Phys 230:4336–4352, 2011) for solving stiff reaction–diffusion equations on high dimensional unstructured meshes. The methods were further extended to solve stiff advection–diffusion–reaction equations in Jiang and Zhang (J Comput Phys 253:368–388, 2013). Recently we studied the computational power of Kr...