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Separation of Variables for Function Generated High-Order Tensors

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Abstract

This article presents a generalization of the adaptive cross approximation to high-order tensors generated by the evaluation of multivariate functions using only a small portion of the original entries. The method is based on dimension trees, which are constructed by inspecting the covariance of the function in order to minimize the approximation rank.

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Notes

  1. Algorithm used: tucker_als, 2010.

  2. Algorithm used: dmrg_cross, Version 2.2, 2012, http://spring.inm.ras.ru/osel/.

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Authors and Affiliations

  1. University of Bonn, Bonn, Germany

    M. Bebendorf & C. Kuske

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  1. M. Bebendorf
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  2. C. Kuske
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Correspondence to M. Bebendorf.

Additional information

This work was supported by the DFG project BE2626/3-1.

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Bebendorf, M., Kuske, C. Separation of Variables for Function Generated High-Order Tensors. J Sci Comput 61, 145–165 (2014). https://doi.org/10.1007/s10915-014-9822-4

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