We consider a two-directional Krylov subspace Kk(A[j], b[j]), where besides the dimensionality k of the subspace increases, the matrix A[j] and vector b[j] which induce the subspace may also augment. Specifically, we consider the case where the matrix A[j] and the vector b[j] are augmented by block triangular bordering. We present a two-directional Arnoldi process to efficiently generate a sequ...

Hydrodynamic interactions play an important role in the dynamics of macromolecules. The most common way to take into account hydrodynamic effects in molecular simulations is in the context of a brownian dynamics simulation. However, the calculation of correlated brownian noise vectors in these simulations is computationally very demanding and alternative methods are desirable. This paper studie...

In recent years, Krylov subspace methods have become popular tools for computing reduced order models of high order linear time invariant systems. The reduction can be done by applying a projection from high order to lower order space using the bases of some subspaces called input and output Krylov subspaces. The aim of this paper is to give an introduction into the principles of Krylov subspac...

In this article we prove the substantiation of the method of averaging for the fuzzy integrodifferential inclusions with small parameter. Thereby we expand a circle of systems to which it is possible to apply Krylov-Bogolyubov method of averaging.

1

We prove various pointwise estimates for solutions of linear elliptic difference inequalities with random coefficients. These estimates include discrete versions of the maximum principle of Aleksandrov and Harnack inequalities and Holder estimates of Krylov and Safonov for elliptic differential operators with bounded coefficients.

For a given real n n matrix A and initial vectors v 1 and w 1 , we examine the sensitivity of the tridiagonal matrix T and the biorthogonal sets of vectors of the Lanczos reduction to small changes in A, v 1 and w 1. We also consider the sensitivity of the developing Krylov subspaces.