In theory, the Lanczos algorithm generates an orthogonal basis of corresponding Krylov subspace. However, in finite precision arithmetic orthogonality and linear independence computed vectors is usually lost quickly. this paper we study a class matrices starting having special nonzero structure that guarantees exact computations whenever floating point satisfying IEEE 754 standard used. Analogo...

In this study, we compute simplicial cohomology groups with different coefficients of a connected sum of certain minimal simple surfaces by using the universal coefficient theorem for cohomology groups. The method used in this paper is a different way to compute digital cohomology groups of minimal simple surfaces. We also prove some theorems related to degree properties of a map on digital sph...

The definition of a commodity component is quite obvious when it comes to the PC as a basic compute engine and building block for clusters of PCs. Looking at the options for a more or less performant interconnect between those compute nodes it is much less obvious which interconnect still qualifies as commodity and which not. We are trying to answer this question based on an in-depth analysis o...

According to the Smoluchowski-Kramers approximation, the solution of the equation μq̈ t = b(q μ t ) − q̇ t + Σ(q t )Ẇt, q 0 = q, q̇ 0 = p converges to the solution of the equation q̇t = b(qt) + Σ(qt)Ẇt, q0 = q as μ → 0. We consider here a similar result for the Langevin process with elastic reflection on the boundary.