Millican Colloquium--Inverse problems and singular value expansions--Mark Gockenbach (Michigan Tech) | Department of Mathematics

COVID-19 updates—In an effort to keep everyone healthy, UNT's on-campus operations are closed until further notice. We're serving students remotely. Please stay connected. Stay up to date on UNT’s response to COVID-19 (Coronavirus).

Have you registered for fall classes yet? While COVID-19 has created some uncertainty for us all, UNT is committed to helping the Mean Green family turn dreams into reality. Let's get through this together!

Register for classes on
Not a UNT student yet? Apply to UNT
Having trouble registering? Get help from an advisor

Millican Colloquium--Inverse problems and singular value expansions--Mark Gockenbach (Michigan Tech)

Event Information
Event Location: 
GAB 461 (Refreshments at 3:30 in 472)
Event Date: 
Monday, March 18, 2019 - 4:00pm

One of the most useful constructs in numerical analysis is the singular value decomposition (SVD) of a matrix, which uses orthogonal transformations to diagonalize the matrix. It has long been known how to extend the SVD to the singular value expansion (SVE) of a compact operator.

In this talk, I will explain why the SVD and SVE are so useful when analyzing linear inverse problems and show how to extend the concept of the SVE to general bounded linear operators defined on Hilbert space.

In certain problems involving a pair of operators, the SVE is not enough. We need a similar construct that allows us to represent the two operators in a consistent form---essentially, to simultaneously diagonalize the two operators. If time permits, I will present the generalized singular value expansion and briefly show how it simplifies the analysis of certain inverse problems.

Thinking about UNT?

It's easy to apply online. Join us and discover why we're the choice of over 38,000 students.

Apply now