CGGC seminar (talk #192)        *** Ph.D. Talk ***
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Date:    Sunday 05/08/2012
Time:    1:00 pm
Room:    Taub 337
Speaker: Uri Itai (Applied Mathematics, Technion)
Title:   Linear Asymptotic Subdivision Schemes for Curves and Positive Definite Matrices
 
Abstract:
 
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
 
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