Knut Hüper and Jochen Trumpf
Newton-type methods on differentiable manifolds became recently very popular, from a theoretical and from an application point of view as well. We discuss invariance properties for these methods on a very rich class of smooth manifolds, namely reductive homogeneous spaces. The invariance properties we present are a generalisation of the well known affine invariance properties of Newton's method on Euclidean spaces. A few examples from signal processing and computer vision are given to explain the details.