Recent results on iteration theory: iteration groups and semigroups in the real case

Iteration Theory and Inequalities for Kleinian Groups

The Newton Iteration on Lie Groups

We de ne the Newton iteration for solving the equation f(y) = 0, where f is a map from a Lie group to its corresponding Lie algebra. Two versions are presented, which are formulated independently of any metric on the Lie group. Both formulations reduce to the standard method in the Euclidean case, and are related to existing algorithms on certain Riemannian manifolds. In particular, we show tha...

On The Convergence Of Modified Noor Iteration For Nearly Lipschitzian Maps In Real Banach Spaces

In this paper, we obtained the convergence of modified Noor iterative scheme for nearly Lipschitzian maps in real Banach spaces. Our results contribute to the literature in this area of re- search.

On Singular Interval-Valued Iteration Groups

Let I = (a,b) and L be a nowhere dense perfect set containing the ends of the interval I and let φ : I → R be a non-increasing continuous surjection constant on the components of I \ L and the closures of these components be the maximal intervals of constancy of . The family F t t R of the interval-valued functions F t 1 φ { , ∈ } (x): = φ [t + φ(x)], x ∈ I forms a set-valued iteration group. W...

On the Relationships Between Power Iteration, Inverse Iteration and FastICA

In recent years, there has been an increasing interest in developing new algorithms for digital signal processing by applying and generalising existing numerical linear algebra tools. A recent result shows that the FastICA algorithm, a popular state-of-the-art method for linear Independent Component Analysis (ICA), shares a nice interpretation as a Newton type method with the Rayleigh Quotient ...