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Techniques for the Reconstruction of a Distribution from a Finite Number of its Moments


Angelov,  I.
Systems and Control Theory, Max Planck Institute for Dynamics of Complex Technical Systems, Max Planck Society;

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John, V., Angelov, I., Öncül, A. A., & Thevenin, D. (2007). Techniques for the Reconstruction of a Distribution from a Finite Number of its Moments. Chemical Engineering Science, 62(11), 2890-2904. doi:10.1016/j.ces.2007.02.041.

The reconstruction of a distribution knowing only a finite number of its moments is an extremely important but in practice still unsolved question for many fields of science (chemical and process engineering, electronic engineering,nuclear physics, image analysis, biotechnology...). Several methods have been proposed and corresponding mathematical formulations have been introduced in the literature during the last decades. Nevertheless, all these are generally limited to particular, often simple cases and require specific assumptions. It is indeed extremely difficult from a theoretical point of view (it is necessary, however not sufficient, that all moments are available for a correct reconstruction) as well as from a practical point of view (ill-posed inverse problem) to find an accurate and relatively fast method which can be applied to all scientific areas. In the present paper, different possible methods (prescribed functions, discrete method,spline-based reconstruction) allowing such a reconstruction are explained,compared in terms of efficiency and accuracy, and validated for chemical engineering applications using examples with different degrees of difficulty. © 2007 Elsevier Ltd. All rights reserved. [accessed 2014 April 1st]