British Library Electronic Table of Contents (United Kingdom)

A one parameter family of iterative methods for the simultaneous approximation of simple complex zeros of a polynomial, based on a cubically convergent Hansen-Patricks family, is studied. We show that the convergence of the basic family of the fourth order can be increased to five and six using Newtons and Halleys corrections, respectively. Since these corrections use the already calculated values, the computational efficiency of the accelerated methods is significantly increased. Further acceleration is achieved by applying the Gauss-Seidel approach (single-step mode). One of the most important problems in solving nonlinear equations, the construction of initial conditions which provide both the guaranteed and fast convergence, is considered for the proposed accelerated family. These cond...

International Nuclear Information System (INIS)

In the case of injuries of the ankle joint, an imaging technique is expected to reveal the state of the bones, ligaments, and articular cartilage. Irrespective of novel imaging techniques, a plain radiography will be made in order to obtain a first picture of the injury. Examples are given, showing that further orientation along the Lauge-Hansen classification scheme of this type of injury helps to completely ascertain the damage to the Articulatio talocruralis. Further examinations applying specific methods such as arthrography will detect possible, isolated syndesmosis ruptures; lesions of the ligaments can also be directly detected by CT or MRT. The articular cartilage and its lesions can be visualized by a combination of CT and arthrography, but are better shown by the completely non-invasive MRT. This latter method also gives insight into pathological processes with the bone. It allows to detect necrotic bone regions and their re-vitalisation in patients with ...