caa a22 4500 44533150X CHVBK 20180317142739.0 cr unu---uuuuu 170323e20110201xx s 000 0 eng 10.1007/s10208-010-9080-2 doi (NATIONALLICENCE)springer-10.1007/s10208-010-9080-2 Convergence and Smoothness of Nonlinear Lane-Riesenfeld Algorithms in the Functional Setting [Elektronische Daten] [Nira Dyn, Ron Goldman] We investigate the Lane-Riesenfeld subdivision algorithm for uniform B-splines, when the arithmetic mean in the various steps of the algorithm is replaced by nonlinear, symmetric, binary averaging rules. The averaging rules may be different in different steps of the algorithm. We review the notion of a symmetric binary averaging rule, and we derive some of its relevant properties. We then provide sufficient conditions on the nonlinear binary averaging rules used in the Lane-Riesenfeld algorithm that ensure the convergence of the algorithm to a continuous function. We also show that, when the averaging rules are C 2 with uniformly bounded second derivatives, then the limit is a C 1 function. Acanonical family of nonlinear, symmetric averaging rules, the p-averages, is presented, and the Lane-Riesenfeld algorithm with these averages is investigated. SFoCM, 2010 Nonlinear subdivision schemes nationallicence Lane-Riesenfeld algorithm nationallicence Data refinement nationallicence Nonlinear symmetric averages nationallicence p -averages nationallicence Convergence and smoothness analysis nationallicence Dyn Nira School of Mathematical Sciences, Tel Aviv University, 69978, Tel Aviv, Israel aut Goldman Ron Department of Computer Science, Rice University, 77251, Houston, TX, USA aut Foundations of Computational Mathematics Springer-Verlag 11/1(2011-02-01), 79-94 1615-3375 11:1<79 2011 11 10208 https://doi.org/10.1007/s10208-010-9080-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10208-010-9080-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Dyn Nira School of Mathematical Sciences, Tel Aviv University, 69978, Tel Aviv, Israel aut NATIONALLICENCE 700 1- Goldman Ron Department of Computer Science, Rice University, 77251, Houston, TX, USA aut NATIONALLICENCE 773 0- Foundations of Computational Mathematics Springer-Verlag 11/1(2011-02-01), 79-94 1615-3375 11:1<79 2011 11 10208 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer