Split Bregman methods are popular iterative for the solution of large-scale minimization problems that arise in image restoration and basis pursuit. This paper investigates possibility projecting into a Krylov subspace fairly small dimension solving problem latter by split algorithm. We concerned with images have been contaminated blur Gaussian or impulse noise. Computed examples illustrate pro...

Many Krylov subspace methods for shifted linear systems take advantage of the invariance of the Krylov subspace under a shift of the matrix. However, exploiting this fact in the non-Hermitian case introduces restrictions; e.g., initial residuals must be collinear and this collinearity must be maintained at restart. Thus we cannot simultaneously solve shifted systems with unrelated right-hand si...

We consider the approximation of the matrix φ-functions that appear in exponential integrators for stiff systems of differential equations. For stiff systems, the field-of-values of the occurring matrices is large and lies somewhere in the left complex half-plane. In order to obtain an efficient method uniformly for all matrices with a field-of-values in the left complex half-plane, we consider...

In this paper we describe and analyze Krylov subspace techniques for accelerating the convergence of waveform relaxation for solving time dependent problems. A new class of accelerated waveform methods, convolution Krylov subspace methods, is presented. In particular, we give convolution variants of the conjugate gradient algorithm and two convolution variants of the GMRES algorithm and analyze...

Many different techniques to reduce the dimensions of a model have been proposed in the near past. Krylov subspace methods are relatively cheap, but generate non-optimal models. In this paper a combination of Krylov subspace methods and Orthonormal Vector Fitting is proposed. In that way an optimal model for a large model can be generated. In the first step, a Krylov subspace method reduces the...

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.

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...

This paper starts oo with studying simple extrapolation methods for the classical iteration schemes such as Richardson, Jacobi and Gauss-Seidel iteration. The extrapolation procedures can be interpreted as approximate minimal residual methods in a Krylov subspace. It seems therefore logical to consider, conversely, classical methods as pre-processors for Krylov subspace methods, as was done by ...