相关论文: When can forward stable algorithms be composed sta…

Quickhull is an algorithm for computing the convex hull of points in a plane that performs well in practice, but has poor complexity on adversarial input. In this paper we show the same holds for the numerical stability of Quickhull.

We consider one variant of stable assignment problems in a bipartite graph endowed with nonnegative capacities on the edges and quotas on the vertices. It can be viewed as a generalization of the stable allocation problem introduced by…

Consider the functional equation ${\mathcal E}_1(f) = {\mathcal E}_2(f) ({\mathcal E})$ in a certain framework. We say a function $f_0$ is an approximate solution of $({\mathcal E})$ if ${\mathcal E}_1(f_0)$ and ${\mathcal E}_2(f_0)$ are…

We introduce a new notion of the stability of computations, which holds under post-processing and adaptive composition. We show that the notion is both necessary and sufficient to ensure generalization in the face of adaptivity, for any…

We report a remarkable type of bifurcation: by varying real parameters, unstable complex orbits may become stable over wide parameter ranges. Thus, phase diagrams obtained by analizing solely the stability of real solutions may be…

We investigate the stability of the wave equation with spatial dependent coefficients on a bounded multidimensional domain. The system is stabilized via a scattering passive feedback law. We formulate the wave equation in a port-Hamiltonian…

This paper investigates the robust stability and stabilization analysis of interval fractional-order systems with time-varying delay. The stability problem of such systems is solved first, and then using the proposed results a stabilization…

Clustering with most objective functions is NP-Hard, even to approximate well in the worst case. Recently, there has been work on exploring different notions of stability which lend structure to the problem. The notion of stability,…

We consider a class of parametrically forced Hamiltonian systems with one-and-a-half degrees of freedom and study the stability of the dynamics when the frequency of the forcing is relatively high or low. We show that, provided the…

We investigate stability of a solution of a hybrid system in the sense that the graphs of solutions from nearby initial conditions remain close and tend towards the graph of the given solution. In this manner, a small continuous-time…

We study a generalization of the classical stable matching problem that allows for cardinal preferences (as opposed to ordinal) and fractional matchings (as opposed to integral). After observing that, in this cardinal setting, stable…

A stability analysis is performed on high-order schemes formulated using the Flux Reconstruction (FR) approach. The one-dimensional advection model equation is used for the assessment of the stability region of these schemes when coupled…

It is discussed and surveyed a numerical method proposed before, that alternative to the usual compression method, provides an approximation to the algorithmic (Kolmogorov) complexity, particularly useful for short strings for which…

Preserving stability is a central problem in data-driven model order reduction of dynamical systems. For linear systems whose dynamics depend on geometric or physical parameters, multivariate rational approximation algorithms such as the…

The issues of robust stability for two types of uncertain fractional-order systems of order $\alpha \in (0,1)$ are dealt with in this paper. For the polytope-type uncertainty case, a less conservative sufficient condition of robust…

A theorem is proved to verify incremental stability of a feedback system via a homotopy from a known incrementally stable system. A first corollary of that result is that incremental stability may be verified by separation of Scaled…

We define a notion of stable and measurable map between cones endowed with measurability tests and show that it forms a cpo-enriched cartesian closed category. This category gives a denotational model of an extension of PCF supporting the…

In this paper we propose a method to define the range of stability of fixed points for a variety of discrete fractional systems of the order $0 < \alpha <2$. The method is tested on various forms of fractional generalizations of the…

We study the stability of holonomic quantum computations with respect to errors in assignment of control parameters. The general expression for fidelity is obtaned. In the small errors limit the simple formulae for the fidelity decrease…

Saddle fixed points are the centerpieces of complicated dynamics in a system. The one-dimensional stable and unstable manifolds of these saddle-points are crucial to understanding the dynamics of such systems. While the problem of sketching…