A new orthogonal projection method for computing the minimum distance between a point and a spatial parametric curve is presented. It consists of a geometric iteration which converges faster than the existing Newton’s method, and it is insensitive to the choice of initial values. We prove that projecting a point onto a spatial parametric curve under the method is globally second-order convergence.

In this paper, we establish a convergence result for equilibria in systems of social interactions with many locally and globally interacting players. Assuming spacial homogeneity and that interactions between different agents are not too strong, we show that equilibria of systems with finitely many players converge to the unique equilibrium of a benchmark system with infinitely many agents. We ...

Giles (Multilevel Monte Carlo path simulation Operations Research, 2008; 56: 607–617) introduced a multi-level Monte Carlo method for approximating the expected value of a function of a stochastic differential equation solution. A key application is to compute the expected payoff of a financial option. This new method improves on the computational complexity of standard Monte Carlo. Giles analy...

We present a new iterative approach for solving linear systems of equations. Our method is inspired by feedback stabilization schemes from robust control and yields a control system, whose parameters can be tuned to achieve prescribed convergence properties. In contrast to well–known iterative solution methods for linear equations from linear algebra, such as GMRES(m) or Arnoldi’s method, the p...

During an interaction people are known to mutually adapt. Phonetic adaptation has been studied notably for prosodic parameters such as loudness, speech rate or fundamental frequency. In most of the cases, results are contradictory and the effectiveness of phonetic convergence during an interaction remains an open issue. This paper describes an experiment based on a children game known as speech...

A new numerical method for an inverse problem for an elliptic equation with unknown potential is proposed. In this problem the point source is running along a straight line and the source-dependent Dirichlet boundary condition is measured as the data for the inverse problem. A rigorous convergence analysis shows that this method converges globally, provided that the so-called tail function is a...

We propose an algorithm-independent framework to equip existing optimization methods with primal-dual certificates. Such certificates and corresponding rate of convergence guarantees are important for practitioners to diagnose progress, in particular in machine learning applications. We obtain new primal-dual convergence rates e.g. for the Lasso as well as many L1, Elastic-Net and group-lasso-r...

The U.S. university-based extension system model has been successful nationally, but not adopted globally. Various historical factors rendered the a less attractive option for emerging post-WWII nations. However, current changes in education and landscapes are creating new opportunities globalization of Extension. Specifically, both Chinese systems now face common challenge delivering meaningfu...

We are interested in the strong convergence and almost sure stability of Euler-Maruyama (EM) type approximations to the solutions of stochastic differential equations (SDEs) with non-linear and nonLipschitzian coefficients. Motivation comes from finance and biology where many widely applied models do not satisfy the standard assumptions required for the strong convergence. In addition we examin...

We develop a semi-discretization approximation for scalar conservation laws with multiple rough time dependence in inhomogeneous fluxes. The method is based on Brenier’s transportcollapse algorithm and uses characteristics defined in the setting of rough paths. We prove strong L-convergence for inhomogeneous fluxes and provide a rate of convergence for homogeneous one’s. The approximation schem...