Inverse and Ill-posed Problems in Banach Lattices: Theory and Applications in Ice Sheet Bed Elevation Measurements

Document Type

Presentation Abstract

Presentation Date

12-10-2012

Abstract

We consider linear inverse problems of form Az = u, z ∈ Z, u ∈ U. Z and U are Banach latices, A is a linear bounded operator. We provide a technique for estimating the error of an approximate solution under some a priori assumptions on the exact solution. The problem of calculating the error estimate is reduced to several linear programming problems.

In the second part of the talk, an application of these techniques to ice sheet bed elevation measurements is considered. We are interested in identifying the ice thickness from the velocity data, weather observations and satellite measurements. Data on ice thickness along certain lines are also available. The problem is to identify the thickness between these lines using the governing equations and some a priori regularity assumptions.

Additional Details

Monday, 10 December 2012
3:10 p.m. in Math 211
4:00 p.m. Refreshments in Math Lounge 109

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