We study the convergence and the stability of fictitious dynamical methods for electrons. First, we show that a particular damped second-order dynamics has a much faster rate of convergence to the ground-state than first-order steepest descent algo...
We study the theory of convergence for CAT$(0)$-lattices (that is groups $Γ$ acting geometrically on proper, geodesically complete CAT$(0)$-spaces) and their quotients (CAT$(0)$-orbispaces). We describe some splitting and collapsing phenomena, expla...
We survey a research program on the strong convergence of unitary and permutation representations of discrete groups. We also take the opportunity to flesh out details that have not appeared elsewhere....
We revisit three classical numerical methods for solving unconstrained optimal control problems - multiple shooting, single shooting, and differential dynamic programming - and examine their local convergence behaviour. In particular, we show that al...
This note gives a few rapidly convergent series representations of the sums of divisors functions. These series have various applications such as exact evaluations of some power series, computing estimates and proving the existence results of some sp...
We are interested in computing a simple eigenpair $(λ,{\bf x})$ of a large non-Hermitian matrix $A$, by a general harmonic Rayleigh-Ritz projection method. Given a search subspace $\mathcal{K}$ and a target point $τ$, we focus on the convergence of...
In mathematics, the convergence condition by Courant–Friedrichs–Lewy (CFL) is a necessary condition for convergence while solving certain partial differential
Thanks for your help! and I'm sorry, what I meant was a sequence in a topological space. I know the examples that you showed me exhibit a non-convergence sequence, but I don't quite see how that …
In the following document, we present a way to obtain the order of convergence of the Fractional Newton-Raphson (F N-R) method, which seems to have an order of convergence at least linearly for the case in which the order $α$ of the derivative is di...
We study the convergence of the population dynamics algorithm, which produces sample pools of random variables having a distribution that closely approximates that of the {\em special endogenous solution} to a stochastic fixed-point equation of the f...
The intrinsic timed-Hausdorff distance between timed-metric spaces, first introduced by Sakovich--Sormani, yields a weak notion of convergence for space-times. In this paper we prove a compactness theorem for the intrinsic timed-Hausdorff convergence...
We develop a framework for proving rapid convergence of shifted QR algorithms which use Ritz values as shifts, in finite arithmetic. Our key contribution is a dichotomy result which addresses the known forward-instability issues surrounding the shift...
In this paper, we establish the local superlinear convergence property of some polynomial-time interior-point methods for an important family of conic optimization problems. The main structural property used in our analysis is the logarithmic homogen...
In this paper we show that numerous patterns exist in the properties of the convergents formed by truncating the Continued Fraction Expansion (CFE) of the Champernowne Constant in base 10 (C10) immediately before the High Water Marks (HWMs). From the...
Algebraic multigrid (AMG) is known to be an effective solver for many sparse symmetric positive definite (SPD) linear systems. For SPD systems, the convergence theory of AMG is well-understood in terms of the $A$-norm, but in a nonsymmetric setting,...
In classical probability theory, the convergence of empirical frequencies to theoretical probabilities: as captured by the Law of Large Numbers (LLN): is treated as axiomatic and emergent from statistical assumptions such as independence and identica...
The terrestrial water cycle links the soil and atmosphere moisture reservoirs through four fluxes: precipitation, evaporation, runoff, and atmospheric moisture convergence (net import of water vapor to balance runoff). Each of these processes is esse...
The TV is dead motto of just a few years ago has been replaced by the prospect of Internet Protocol (IP) television experiences over converged networks to become one of the great technology opportunities in the next few years. As an introduction to t...
The classic paper by Fleming, Mehen and Stewart cast doubts on the convergence of spin-triplet nucleon-nucleon partial wave scattering amplitudes when following the proposal of Kaplan, Savage and Wise to construct nuclear effective field theory aroun...
Often in the analysis of first-order methods, assuming the existence of a quadratic growth bound (a generalization of strong convexity) facilitates much stronger convergence analysis. Hence the analysis is done twice, once for the general case and on...