ALTERNATING MINIMAL ENERGY METHODS FOR LINEAR SYSTEMS IN HIGHER DIMENSIONS∗

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Alternating Minimal Energy Methods for Linear Systems in Higher Dimensions (2013, unknown): “In Section 3 we propose the AMEn algorithm, then we compare it with similar algorithms from [9] and prove the convergence theorem.”
Tensor Ring Decomposition (2016, methodology): “At the same time, new tensor formats have been proposed, e.g. the quantized tensor train (QTT) [42], [43] and the QTT-Tucker [44], which have been also applied to large-scale optimization problems [41], [45], [46].”
Hand-waving and interpretive dance: an introductory course on tensor networks (2016, background): “13 There are however somewhat involved methods that allow for auxiliary data to be injected in a non-local fashion such as [55, 56] (see [57] for a review), achieving a similar goal.”
Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 2 Applications and Future Perspectives (2017, methodology): “This problem can be formulated as the standard symmetric eigenvalue decomposition (EVD), in the form A xk = λkxk, k = 1, 2, . . . , K, (3.21) where xk P RI are the orthonormal eigenvectors and λk the corresponding eigenvalues of a symmetric matrix A P RIˆI .”