Math Modeling
Seminar
Regularization of the
Factorization Method with
Applications
Dr. Isaac
Harris
Assistant
Professor
Department of
Mathematics
Purdue
University
You may attend this
lecture in person at 2300 Gosnell Hall or virtually via
Zoom.
If you’d like to
attend virtually, you may register here
for Zoom link.
Abstract:
In this talk, we discuss
a new regularized version of the Factorization Method. The Factorization
Method uses Picard’s Criteria to define an indicator function to image
an unknown region. In most applications, the data operator is compact
which gives that the singular values can tend to zero rapidly which can
cause numerical instabilities. The regularization of the Factorization
Method presented here seeks to avoid the numerical instabilities in
applying Picard’s Criteria. This method allows one to image the
interior structure of an object with little a priori information in a
computationally simple and analytically rigorous way. Here we will focus
on an application of this method to diffuse optical tomography which will
prove that this method can be used to recover an unknown subregion from
the Dirichlet-to-Neumann mapping.
Speaker
Bio:
As an undergraduate, my
favorite class was Differential Equations. One of the things that
fascinated me about the class was how different areas of mathematics came
together to solve interesting problems. Ideas from Calculus and Linear
Algebra were no longer separate entities but part of something bigger.
Being able to study different applications of mathematics as a McNair
Scholar help me cultivate my interest in mathematics. After graduating
from the University of Delaware I was a postdoc at Texas A&M
university then I joined Purdue’s Mathematics Department in Fall 2018
as an Assistant Professor. This was an exciting prospect where I could
join a department with extremely talented mathematicians from many
different fields.
Intended
Audience:
Undergraduates,
graduates, and experts. Those with interest in the topic.
The Math Modeling
Seminar will recur each week throughout the semester on the same day and
time. Find out more about upcoming speakers on the Mathematical Modeling Seminar Series
webpage.
To request an
interpreter, please visit myaccess.rit.edu
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