We re-examine a fixed-point algorithm proposed by Hyvarinen for independent component analysis, wherein local convergence is proved subject to an ideal signal model using a square invertible mixing matrix. Here, we derive step-size bounds which ensure monotonic convergence to a local extremum for any initial condition. Our analysis does not assume an ideal signal model but appeals rather to pro...

|The magnitude of the lters associated with Daubechies' wavelets is shown to converge to an ideal high-pass lter when the length of the support of the wavelets increases to 1. The convergence of the lters is monotonic. That is, the larger support of a Daubechies' wavelet, the better quality of the lter associated with. The rate of the convergence is also given. The magnitude of the lter associa...

*Correspondence: [email protected] 1Department of Mathematics, Rajiv Gandhi University, Rono Hills, Doimukh, Arunachal Pradesh 791112, India Full list of author information is available at the end of the article Abstract An ideal I is a family of subsets of positive integers N×N which is closed under taking finite unions and subsets of its elements. In this paper, we present some definitions w...

Infinitesimal robustness employs first order asymptotics to derive results on uniform (weak) convergence on shrinking neighborhoods around an ideal central model. In the case of the median in the one–dimensional location setup, we refine such a result concerning the convergence of the MSE, proceeding to higher order asymptotics — up to order 1/n , for sample size n . In contrast to usual higher...

The concept of I-convergence was introduced by Kostyrko et al (2001).It seems therefore reasonable to investigate the concept of I -convergence for the double sequences in 2-normed spaces.In this article we define and investigate ideal analogue of convergence for double sequences in 2-normed space and so we extend this concepts to I2-limit points and I2-cluster points in this spaces.We prove so...

Identifying convergence in numerical optimization is an ever-present, difficult, and often subjective task. The statistical framework of Gaussian process surrogate model optimization provides useful measures for tracking optimization progress; however, the identification of convergence via these criteria has often provided only limited success and often requires a more subjective analysis. Here...