[Amath-seminars] SIAM PNW Webinar Thursday at 3pm in Wan Conference
Randall J LeVeque
rjl at uw.edu
Tue Dec 5 20:11:34 PST 2017
This Thursday at 3pm Jodi Mead from Boise State University will be giving
the first SIAM Pacific Northwest Section
<https://sites.google.com/site/siampnwsection/home> talk of the year.
These talks are meant to bring together the SIAM community in our broad
geographic region and happen once per quarter.
This online talk will be broadcast in the Wan Conference Room (Lewis 208),
please join in! Or GoToMeeting information is at the end of this message.
The next talk in the series
<https://sites.google.com/site/siampnwsection/seminar-series> will be by
Leah Keshet from UBC on January 11 at 3pm.
Speaker: Professor Jodi Mead <http://math.boisestate.edu/~mead/>, Boise
Time: Thursday, December 7, 3pm PST
Title: Singular value analysis of Joint Inversion
Abstract: The degree of ill-posedness of the linear operator equation Ax =
b can be measured by the decay rate of the singular values of A. If the
inverse problem is nonlinear and A is the corresponding Jacobian matrix,
the singular values measure the local ill-posedness of the problem. We
consider the case where the operator A is compact and maps infinite
dimensional Hilbert spaces. The degree of ill-posedness can be measured by
μ, where the singular values σ_n(A) ≈ n^(−μ). The problem becomes more
difficult to solve numerically with increasing μ.
When the singular values quickly decay to zero, it is common to truncate
them or introduce a regularization term. However, if the problem is
severely ill-posed, a large amount of regularization may be required to
solve the problem, and this can introduce significant bias error in the
solution estimate. Regularization can be viewed as adding information to
the ill-posed problem, and hence we consider the regularized inverse
problem as simultaneous joint inversion. Simultaneous joint inversion has
recently become a common method to incorporate multiple types of data and
physics in a single inversion.
We extend discrete techniques of stacking matrices in joint inversion, to
combining Green’s function solutions of multiple differential equations
representing different types of data. The singular values of the joint
operators indicate the effectiveness of combining multiple types of
physics. This knowledge provides mathematical justification for joint
inversion, and can be determined before the complicated machinery of
discretizing and solving the problem is implemented. We will give an
example of two differential equations with known Green’s function
solutions. The decay rate of the singular values of the individual
operators are compared to the singular values of the joint operator, and
the extent to which the ill-posedness was resolved is quantified.
This is joint work with James Ford.
SIAM PNW Section Seminar by Jodi Mead
Thu, Dec 7, 2017 3:00 PM - 4:00 PM PST
Please join my meeting from your computer, tablet or smartphone.
You can also dial in using your phone.
United States: +1 (872) 240-3412 <+1%20872-240-3412>
Access Code: 452-039-061
First GoToMeeting? Let's do a quick system check: https://link.gotomeetin
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