A new method for reconstruction of cross-sections using Tucker decomposition

Abstract : The full representation of a d-variate function requires exponentially storage size as a function of dimension d and high computational cost. In order to reduce these complexities, function approximation methods (called reconstruction in our context) are proposed, such as: interpolation, approximation, etc. The traditional interpolation model like the multilinear one, has this dimensional-ity problem. To deal with this problem, we propose a new model based on the Tucker format-a low-rank tensor approximation method, called here the Tucker decomposition. The Tucker decomposition is built as a tensor product of one-dimensional spaces where their one-variate basis functions are constructed by an extension of the KarhunenLò eve decomposition into high-dimensional space. Using this technique, we can acquire, direction by direction, the most important information of the function and convert it into a small number of basis functions. Hence, the approximation for a given function needs less data than that of the multilinear model. Results of a test case on the neutron cross-section reconstruction demonstrate that the Tucker decomposition achieves a better accuracy while using less data than the multilinear interpolation.
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Submitted on : Wednesday, March 8, 2017 - 5:23:24 PM
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  • HAL Id : hal-01485419, version 1

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Thi Hieu Luu, Yvon Maday, Matthieu Guillo, Pierre Guérin. A new method for reconstruction of cross-sections using Tucker decomposition. 2017. ⟨hal-01485419⟩

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