A convergence theory for saddle functions

A Convergence Theory for Saddle Functions

We develop a convergence theory called epi/hypo-convergence, for bivariate functions that essentially implies the convergence of their saddle points. We study the properties of this limiting process in particular. We characterize the limit functions associated to any collection of bivariate functions and obtain a compactness theorem for the space of saddle functions. Even when restricted to the...

L ∞ - convergence of saddle - point approximations for second order problems

Adaptive Wavelet Methods for Saddle Point Problems - Optimal Convergence Rates

In this paper an adaptive wavelet scheme for saddle point problems is developed and analysed. Under the assumption that the underlying continuous problem satisfies the inf-sup condition it is shown in the first part under which circumstances the scheme exhibits asymptotically optimal complexity. This means that within a certain range the convergence rate which relates the achieved accuracy to t...

Divided Saddle Theory: A New Idea for Rate Constant Calculation.

We present a theory of rare events and derive an algorithm to obtain rates from postprocessing the numerical data of a free energy calculation and the corresponding committor analysis. The formalism is based on the division of the saddle region of the free energy profile of the rare event into two adjacent segments called saddle domains. The method is built on sampling the dynamics within these...

On The Mean Convergence of Biharmonic Functions

Let denote the unit circle in the complex plane. Given a function , one uses t usual (harmonic) Poisson kernel for the unit disk to define the Poisson integral of , namely . Here we consider the biharmonic Poisson kernel for the unit disk to define the notion of -integral of a given function ; this associated biharmonic function will be denoted by . We then consider the dilations ...