TY - GEN

T1 - A Posteriori Error Estimates for Fredholm Integral Equations of the First Kind

AU - Koshev, N.

AU - Beilina, L.

PY - 2013

Y1 - 2013

N2 - We consider an adaptive finite element method for the solution of a Fredholm integral equation of the first kind and derive a posteriori error estimates both in the Tikhonov functional and in the regularized solution of this functional. We apply nonlinear results obtained in Beilina et al., (Journal of Mathematical Sciences, 167, 279-325, 2010), Beilina and Klibanov, (Inverse Problems, 26, 045012, 2010), Beilina et al., (Journal of Mathematical Sciences, 172, 449-476, 2011), Beilina and Klibanov, (Inverse Problems, 26, 125009, 2010), Klibanov et al., (Inverse and Ill-Posed Problems), 19, 83-105, 2011) for the case of the linear bounded operator. We formulate an adaptive algorithm and present experimental verification of our adaptive technique on the backscattered data measured in microtomography.

AB - We consider an adaptive finite element method for the solution of a Fredholm integral equation of the first kind and derive a posteriori error estimates both in the Tikhonov functional and in the regularized solution of this functional. We apply nonlinear results obtained in Beilina et al., (Journal of Mathematical Sciences, 167, 279-325, 2010), Beilina and Klibanov, (Inverse Problems, 26, 045012, 2010), Beilina et al., (Journal of Mathematical Sciences, 172, 449-476, 2011), Beilina and Klibanov, (Inverse Problems, 26, 125009, 2010), Klibanov et al., (Inverse and Ill-Posed Problems), 19, 83-105, 2011) for the case of the linear bounded operator. We formulate an adaptive algorithm and present experimental verification of our adaptive technique on the backscattered data measured in microtomography.

UR - http://www.scopus.com/inward/record.url?scp=84893495254&partnerID=8YFLogxK

U2 - 10.1007/978-1-4614-7816-4_5

DO - 10.1007/978-1-4614-7816-4_5

M3 - Conference contribution

AN - SCOPUS:84893495254

SN - 9781461478157

T3 - Springer Proceedings in Mathematics and Statistics

SP - 75

EP - 93

BT - Applied Inverse Problems - Select Contributions from the First Annual Workshop on Inverse Problems

T2 - 1st Annual Workshop on Inverse Problems

Y2 - 2 June 2011 through 3 June 2011

ER -