Related papers: Equivalence Theorems in Numerical Analysis : Integ…
Although the \emph{residual method}, or \emph{constrained regularization}, is frequently used in applications, a detailed study of its properties is still missing. This sharply contrasts the progress of the theory of Tikhonov…
We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is…
The stability of stationary solutions of first-order systems of PDE's are considered. They may include some singular geometric terms, leading to discontinuous flux and non-conservative products. Based on several examples in Fluid Mechanics,…
Numerical Analysts and scientists working in applications often observe that once they improve their techniques to get a better accuracy, some instability creeps in through the back door. This paper shows for a large class of numerical…
Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…
In this work, we address the problem of polynomial interpolation of non-pointwise data. More specifically, we assume that our input information comes from measurements obtained on diffuse compact domains. Although the nodal and the diffused…
A new equivalence notion between non-stationary subdivision schemes, termed asymptotical similarity, which is weaker than asymptotical equivalence, is introduced and studied. It is known that asymptotical equivalence between a…
It is often the case in numerical relativity that schemes that are known to be convergent for well posed systems are used in evolutions of weakly hyperbolic (WH) formulations of Einstein's equations. Here we explicitly show that with…
In this paper, we study the existence and the stability in the sense of Lyapunov of solutions for\ differential inclusions governed by the normal cone to a prox-regular set and subject to a Lipschitzian perturbation. We prove that such,…
The goal of this paper is twofold. First, we present a unified way of formulating numerical integration problems from both approximation theory and discrepancy theory. Second, we show how techniques, developed in approximation theory, work…
Von Neumann established that discretized algebraic equations must be consistent with the differential equations, and must be stable in order to obtain convergent numerical solutions for the given differential equations. The "stability" is…
In contrast to the prevailing view in the literature, it is shown that even extremely stiff sets of ordinary differential equations may be solved efficiently by explicit methods if limiting algebraic solutions are used to stabilize the…
In the context of mathematical modeling, it is sometimes convenient to integrate models of different nature. These types of combinations, however, might entail difficulties even when individual models are well-understood, particularly in…
One of the main reasons for topological persistence being useful in data analysis is that it is backed up by a stability (isometry) property: persistence diagrams of $1$-parameter persistence modules are stable in the sense that the…
Polynomial stability of exact solution and modified truncated Euler-Maruyama method for stochastic differential equations with time-dependent delay are investigated in this paper. By using the well known discrete semimartingale convergence…
Concepts like `typicality' and the `eigenstate thermalization hypothesis' aim at explaining the apparent equilibration of quantum systems, possibly after a very long time. However, these concepts are not concerned with the specific way in…
Solving inverse problems \(Ax = y\) is central to a variety of practically important fields such as medical imaging, remote sensing, and non-destructive testing. The most successful and theoretically best-understood method is convex…
In this paper, we establish coincidence-like results in the case when the values of the correspondences are not convex. In order to do this, we define a new type of correspondences, namely properly quasi-convex-like. Further, we apply the…
We will prove the equivalence of three methods, the so called energy methods, for establishing the stability of an equilibrium point for a dynamical system. We will illustrate by examples that this result simplifies enormously the amount of…
We present intersection type systems in the style of sequent calculus, modifying the systems that Valentini introduced to prove normalisation properties without using the reducibility method. Our systems are more natural than Valentini's…