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Asymptotic behaviour of the minimum bound method for choosing the regularization parameter
Journal article   Open access   Peer reviewed

Asymptotic behaviour of the minimum bound method for choosing the regularization parameter

M.A. Lukas
Inverse Problems, Vol.14(1), pp.149-159
1998
DOI: https://doi.org/10.1088/0266-5611/14/1/013
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Abstract

We consider a parameter choice method (called the minimum bound method) for regularization of linear ill-posed problems that was developed by Raus and Gfrerer for the case with continuous, deterministic data. The method is adapted and analysed in a discrete, stochastic framework. It is shown that asymptotically, as the number of data points approaches infinity, the method (with a constant set to 2) behaves like an unbiased error method, which selects the parameter by minimizing a certain unbiased estimate of the expected squared error in the regularized solution. The method is also shown to be weakly asymptotically optimal, in that the 'expected' estimate achieves the optimal rate of convergence with repect to the expected squared error criterion and it has the optimal rate of decay.

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Citation topics
9 Mathematics
9.162 Numerical Methods
9.162.1492 Inverse Problems
Web Of Science research areas
Mathematics, Applied
Physics, Mathematical
ESI research areas
Physics
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