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TUCKER_ALS computes the best rank-(R1,R2,..,Rn) approximation of tensor X, according to the specified dimensions. I am using MATLAB Tensor Toolbox Version 2.5. I am wondering if I write a paper, how can I refer to the algorithm?

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Kolda (one of the authors of the MATLAB Tensor Toolbox) also wrote a review paper in SIREV called Tensor Decompositions and Applications that provides references for algorithms that are at least related. (Without looking at the source, I can't say if they're the same.) You could try looking at Section 4, particularly Section 4.3, for useful references.

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