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The Lane-Riesenfeld Algorithm and its extensions
Host: Prof. Kai Hormann
Thursday
16.05
USI Lugano Campus, room A-14, Red building
15:30-16:30
Nira Dyn
Tel Aviv University, Israel
Abstract:
The talk presents the linear Lane-Riesenfeld (LR) algorithm and describes our general method for extending it. In the case that the binary linear averages of numbers in the linear LR algorithm are replaced by binary, symmetric non-linear averages, our main achievement is the proof that the limits of this extended non-linear LR algorithm have the same smoothness as that of the limits of the linear LR algorithm. The proof is based on the observation that any such non-linear algorithm can be regarded as a non-uniform linear subdivision scheme depending on the initial data, and can be analyzed by our tools for non-uniform linear schemes.
Biography:
Nira Dyn is an expert in geometric modeling, subdivision surfaces, approximation theory, and image compression. She is a professor emeritus of applied mathematics at Tel Aviv University and has been called a "pioneer and leading researcher in the subdivision community". She earned a bachelor's degree from the Technion in 1965 and went on to graduate study at the Weizmann Institute of Science, where she earned a master's degree in 1967 and completed her doctorate in 1970. After postdoctoral research in the Institute of Fundamental Studies at the University of Rochester, she joined the Tel Aviv faculty in 1972, and retired in 2010. She has published more than 180 papers in the scientific literature and 2 influential books.