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The Taub Faculty of Computer Science Events and Talks

CGGC Seminar: Linear Asymptotic Subdivision Schemes for Curves and Positive Definite Matrices
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Uri Itai (Applied Mathematics, Technion)
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Sunday, 05.08.2012, 13:00
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Room 337-8 Taub Bld.
Subdivision schemes are attractive methods for generating a smooth object from discrete data by repeating refinements. These schemes have many desirable properties such as fast convergence and smoothness of the generated objects. Therefore, subdivision schemes have gained popularity in recent years as an important tool in approximation theory, computer graphics, geometric design and computer aided design. I will start with a survey on basic subdivision schemes. Then, I will review fundamental results in the field, and will go over the needed material to generalize those schemes to refinements of curves and matrices.

The two generalizations are constructing a surface from sampled curves and generating a matrix ``curves" from a sequence of linearly ordered symmetric positive definite matrices. In both cases we proved convergence to a smooth limit. Additional properties of each object will be presented. Future research ideas and insight on the field will end the talk. No prior knowledge in the field will be assumed.

This talk summarizes the Ph.D research of the speaker under the supervision of Prof. Gershon Elber and Prof. Nira Dyn.