For strongly directed anisotropic processes such as coherence-enhancing di usion ltering it is crucial to use numerical schemes with highly accurate directional behavior. We show that this is not possible in a satisfactory way when discretizations are limited to 3 3 stencils. As a consequence, we investigate a novel algorithm based on 5 5 stencils. It utilizes recently discovered di erentiation...

This paper is concerned with the global asymptotic stability of the zero solution of the half-linear differential system x′ = − e(t)x+ f(t)φp∗(y) , y′ = − g(t)φp(x)− h(t)y , where p > 1, p∗ > 1 (1/p + 1/p∗ = 1), and φq(z) = |z|q−2z for q = p or q = p∗. The coefficients are not assumed to be positive. This system includes the linear differential system x′ = A(t)x with A(t) being a 2 × 2 matrix a...

In this paper we introduce a new procedure called α -Discounting Method for MultiCriteria Decision Making (α-D MCDM), which is as an alternative and extension of Saaty’s Analytical Hierarchy Process (AHP). It works for any number of preferences that can be transformed into a system of homogeneous linear equations. A degree of consistency (and implicitly a degree of inconsistency) of a decision-...

In this paper we show that every diffusive system is a well-posed system in the sense of Salamon and Weiss. Furthermore, we characterize several systems theoretic properties of these systems, such as stability, controllability, and observability. Instead of referring to general results on well-posed linear system, we prove these results directly. Hence we hope that this paper will serve as a tu...

For block-tridiagonal linear system of equations, a variant of tangential filtering preconditioners is proposed in this paper. The new variant is based on a twisted block factorization along with certain filtering property. For practical usage, a class of composite preconditioners tested, which are constructed by combining the twisted tangential filtering decomposition preconditioner with the c...

The adjoint linear system on a surface have been studied by many authors. Among these, Reider’s criterion on a smooth surface is very famous. Here we prove a similar criterion on normal surfaces.

In the present paper, we present smoothing procedures for iterative block methods for solving nonsymmetric linear systems of equations with multiple right-hand sides. These procedures generalize those known when solving one right-hand linear systems. We give some properties of these new methods and then, using these procedures we show connections between some known iterative block methods. Fina...

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How would you try to solve a linear system of equations with more unknowns than equations? Of course, there are infinitely many solutions, and yet this is the sort of the problem statisticians face with many modern datasets, arising in genetics, imaging, finance and many other fields. What’s worse, our equations are often corrupted by noisy measurements! In this article we will introduce a stat...

We consider a standard splitting algorithm for the rare-event simulation of overflow probabilities in any subset of stations in a Jackson network at level n, starting at a fixed initial position. It was shown in [8] that a subsolution to the Isaacs equation guarantees that a subexponential number of function evaluations (in n) suffice to estimate such overflow probabilities within a given relat...