A recent paper introduced the network element method (NEM) where usual mesh was replaced by a discretization network. Using associated geometric coefficients and following virtual framework, consistent stable numerical scheme proposed. The aim of present is to derive convergence theory for NEM under mild assumptions on exact problem. We also basic error estimates, which are sub-optimal in sense...

We extend the Lp theory of sparse graph limits, which was introduced in a companion paper, by analyzing different notions of convergence. Under suitable restrictions on node weights, we prove the equivalence of metric convergence, quotient convergence, microcanonical ground state energy convergence, microcanonical free energy convergence, and large deviation convergence. Our theorems extend the...

Curve evolution is often used to solve computer vision problems. If the curve evolution fails to converge, we would not be able to solve the targeted problem in a lifetime. This paper studies the theoretical aspect of the convergence of a type of general curve evolutions. We establish a theory for analyzing and improving the stability of the convergence of the general curve evolutions. Based on...

This paper deenes a class of evolutionary algorithms called evolutionary pattern search algorithms (EPSAs) and analyzes their convergence properties. This class of algorithms is closely related to evolutionary programming, evolution strategie and real-coded genetic algorithms. EPSAs are self-adapting evolutionary algorithms that modify the step size of the mutation operator in response to the s...