# Bibliography

Journal Article

### Low Complexity Damped Gauss-Newton algorithms for CANDECOMP/PARAFAC

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**: **SIAM Journal on Matrix Analysis and Applications vol.34, 1 (2013), p. 126-147

**: **1M0572, GA MŠk,
GA102/09/1278, GA ČR

**: **tensor factorization,
canonical polyadic decomposition,
alternating least squares

**: **http://library.utia.cas.cz/separaty/2014/SI/tichavsky-0391019.pdf

**(eng): **The damped Gauss-Newton (dGN) algorithm for CANDECOMP/PARAFAC (CP) decomposition can handle the challenges of factors and different magnitudes of factors; nevertheless, for factorization of an order-N tensor of size I_1×I_2 ×• • •×I_N with rank R, the algorithm is computationally demanding due to construction of large approximate Hessian of size (RT × RT) and its inversion where T= sum_n I_n. In this paper, we propose a fast implementation of the dGN algorithm which is based on novel expressions of the inverse approximate Hessian in block form. The new implementation has lower computational complexity, besides computation of the gradient, requiring the inversion of a matrix of size NR^2xNR^2, which is smaller than the whole approximate Hessian, if T>NR. In addition, neither the Hessian nor its inverse never needs to be stored in its entirety. A variant of the algorithm working with complex-valued data is proposed as well.

**: **BB