Publica
Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. Spectral Radii of Asymptotic Mappings and the Convergence Speed of the Standard Fixed Point Algorithm
 Institute of Electrical and Electronics Engineers IEEE; IEEE Signal Processing Society: IEEE International Conference on Acoustics, Speech, and Signal Processing 2018. Proceedings : April 1520, 2018, Calgary Telus Convention Center, Calgary, Alberty, Canada Piscataway, NJ: IEEE, 2018 ISBN: 9781538646588 ISBN: 9781538646571 ISBN: 9781538646595 pp.45094513 
 International Conference on Acoustics, Speech, and Signal Processing (ICASSP) <2018, Calgary> 

 English 
 Conference Paper 
 Fraunhofer HHI () 
Abstract
Important problems in wireless networks can often be solved by computing fixed points of standard or contractive interference mappings, and the conventional fixed point algorithm is widely used for this purpose. Knowing that the mapping used in the algorithm is not only standard but also contractive (or only contractive) is valuable information because we obtain a guarantee of geometric convergence rate, and the rate is related to a property of the mapping called modulus of contraction. To date, contractive mappings and their moduli of contraction have been identified with casebycase approaches that can be difficult to generalize. To address this limitation of existing approaches, we show in this study that the spectral radii of asymptotic mappings can be used to identify an important subclass of contractive mappings and also to estimate their moduli of contraction. In addition, if the fixed point algorithm is applied to compute fixed points of positive concave mappings, we show that the spectral radii of asymptotic mappings provide us with simple lower bounds for the estimation error of the iterates. An immediate application of this result proves that a known algorithm for load estimation in wireless networks becomes slower with increasing traffic.