This paper studies the equivalence of exponential ergodicity and L-exponential convergence mainly for continuous-time Markov chains. In the reversible case, we show that the known criteria for exponential ergodicity are also criteria for L-exponential convergence. Until now, no criterion for L-exponential convergence has appeared in the literature. Some estimates for the rate of convergence of ...

In total variation denoising, one attempts to remove noise from a signal or image by solving a nonlinear minimization problem involving a total variation criterion. Several approaches based on this idea have recently been shown to be very eeective, particularly for denoising functions with discontinuities. This paper analyzes the convergence of an iterative method for solving such problems. The...

Convergence is emerging around the world as a result of development of technology and market demand. Serving as a high performance of telecommunications, it can greatly improve socioeconomic development in developing countries according to the theory of telecommunications and economic development. Convergence is occurring in China with China’s fast economic development and market growth. China ...

The mean shift iterative algorithm was proposed in 2006, for using the entropy as a stopping criterion. From then on, a theoretical base has been developed and a group of applications has been carried out using this algorithm. This paper proposes a new stopping criterion for the mean shift iterative algorithm, where stopping threshold via entropy is used now, but in another way. Many segmentati...

I propose a new definition of identification in the limit (also called convergence to the truth), as a new success criterion that is meant to complement, rather than replacing, the classic definition due to Gold (1967). The new definition is designed to explain how it is possible to have successful learning in a kind of scenario that Gold’s classic account ignores—the kind of scenario in which ...

We recently proposed a new incremental procedure for supervised learning with noisy data. Each step consists in adding to the current network a new unit (or small 2-or 3-neuron networks) which is trained to learn the error of the network. The incremental step is repeated until the error of the current network can be considered as a noise. The stopping criterion is very simple and can be directl...

We study the convergence of consensus algorithms in wireless sensor networks with random topologies where the instantaneous links exist with a given probability and are allowed to be spatially correlated. Aiming at minimizing the convergence time of the algorithm, we adopt an optimization criterion based on the spectral radius of a positive semidefinite matrix for which we derive closed-form ex...