Optimization via Separated Representations and the Canonical Tensor Decomposition

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Reynolds, Matthew J; Beylkin, Gregory; Doostan, Alireza;
  • Related identifiers: doi: 10.1016/j.jcp.2017.07.012
  • Subject: Mathematics - Optimization and Control | Mathematics - Numerical Analysis
    acm: MathematicsofComputing_NUMERICALANALYSIS | ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION

We introduce a new, quadratically convergent algorithm for finding maximum absolute value entries of tensors represented in the canonical format. The computational complexity of the algorithm is linear in the dimension of the tensor. We show how to use this algorithm to... View more
  • References (26)
    26 references, page 1 of 3

    [1] B. Alpert. A class of bases in L2 for the sparse representation of integral operators. SIAM J. Math. Anal, 24(1):246-262, 1993.

    [2] B. Alpert, G. Beylkin, D. Gines, and L. Vozovoi. Adaptive solution of partial differential equations in multiwavelet bases. J. Comput. Phys., 182(1):149-190, 2002.

    [3] T. Bäck. Evolutionary algorithms in theory and practice: evolution strategies, evolutionary programming, genetic algorithms. Oxford University Press, 1996.

    [4] G. Beylkin, J. Garcke, and M. J. Mohlenkamp. Multivariate regression and machine learning with sums of separable functions. SIAM Journal on Scientific Computing, 31(3):1840-1857, 2009.

    [5] G. Beylkin and M. J. Mohlenkamp. Numerical operator calculus in higher dimensions. Proc. Natl. Acad. Sci. USA, 99(16):10246-10251, August 2002.

    [6] G. Beylkin and M. J. Mohlenkamp. Algorithms for numerical analysis in high dimensions. SIAM J. Sci. Comput., 26(6):2133-2159, July 2005.

    [7] G. Beylkin and L. Monzón. Approximation of functions by exponential sums revisited. Appl. Comput. Harmon. Anal., 28(2):131-149, 2010.

    [8] D. J. Biagioni, D. Beylkin, and G. Beylkin. Randomized interpolative decomposition of separated representations. Journal of Computational Physics, 281:116-134, 2015.

    [9] R. Bro. Parafac. Tutorial & Applications. In Chemom. Intell. Lab. Syst., Special Issue 2nd Internet Conf. in Chemometrics (incinc'96), volume 38, pages 149-171, 1997. http://www.models.kvl.dk/users/rasmus/presentations/parafac_tutorial/paraf.htm.

    [10] J. D. Carroll and J. J. Chang. Analysis of individual differences in multidimensional scaling via an N-way generalization of Eckart-Young decomposition. Psychometrika, 35:283-320, 1970.

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