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14:20 - 15:20, July 16, 2015 (Thursday)
R202, Astronomy-Mathematics Building, NTU
(台灣大學天文數學館 202室)
Increasing stability in inverse problems
Ru-Yu Lai (University of Minnesota)

The problem of recovering potential in the Schrödinger equation from boundary measurements has been studied since the 1980s. It is well known that a logarithmic stability estimate holds and is optimal. However, the logarithmic stability makes it difficult to design reliable reconstruction algorithms in practice since small errors in the data of the inverse problem result in large error in numerical reconstruction of physical properties of the medium. It has been observed numerically that the stability increases if one increases the frequency in some cases. In this talk, I will introduce several results which rigorously demonstrated the increasing stability behavior in different settings. 


 

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