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Local stability and estimation of uncertainty for solutions to inverse problems |
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| Authors: | Alexey I Yaremchuk Maxim I Yaremchuk Jens Schröter Martin Losch |
| Institution: | (1) Andreyev Acoustics Institute, Moscow, Russia, RU;(2) International Pacific Research Center, University of Hawaii, USA, US;(3) Alfred-Wegener-Institut für Polar- und Meeresforschung, Bremerhaven, Germany, DE |
| Abstract: | We present a method for studying local stability of a solution to an inverse problem and evaluate the uncertainty in determining true values of particular observables. The investigation is done under the assumption that only the Gaussian part of fluctuations about the local minimum of the cost (likelihood) function is essential. Our approach is based on the spectral analysis of the Hessian operator associated with the cost function at its extremal point, and we put forward an effective iterative algorithm suitable for numerical implementation in the case of a computationally large problem. Received: 16 May 2001 / Accepted: 22 October 2001 |
| Keywords: | Inverse modelling Hessian operator Spectral analysis Error covariance Polynomial expansion |
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