PhD Dissertation Defense: “Condition-dependent Hilbert Spaces for Gradient Descent and Application to the Tricomi Equation” | Department of Mathematics
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PhD Dissertation Defense: “Condition-dependent Hilbert Spaces for Gradient Descent and Application to the Tricomi Equation”

Event Information
Speaker: 
Jason Montgomery
Event Location: 
GAB 461
Event Date: 
Thursday, June 5, 2014 - 3:00pm

Professor John Neuberger invites you to attend the PhD dissertation defense of Jason Montgomery next Thursday, June 5th at 3:00 pm in GAB 461. Cake and coffee will be served in GAB 472 following this event.

"Condition-dependent Hilbert Spaces for Gradient Descent and Application to the Tricomi Equation"

Abstract:

An iterative gradient descent method is constructed for application to linear differential equations paired with uniqueness-inducing supplementary conditions, e.g., boundary conditions. For well-posed problems, the method produces the unique solution with the first iteration. For overdetermined problems, the method converges to the unique element in the kernel of the differential operator so that change in condition values is minimal. The method is applied to the Tricomi equation in an investigation of which conditions are necessary and sufficient for existence and uniqueness on mixed rectangular domains.