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Comparing different types of approximators for choosing the parameters in the regularization of ill-posed problems. (English) Zbl 1069.65146

Summary: Regularized approximations to the solutions of ill-posed problems typically vary from over-smoothed, inaccurate reconstructions to under-smoothed and unstable solutions as the regularization parameter varies about its optimal value.
It thus makes sense to compare two (or more) regularized approximations, and seek the parametervalues where the distance between the approximations is a minimum.
This paper advances the theory and practice of this methodology. The method appears to work very well and be very stable, particularly in the presence of extreme error levels.

MSC:

65R20 Numerical methods for integral equations
45B05 Fredholm integral equations
65R30 Numerical methods for ill-posed problems for integral equations
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