The hierarchical SVD provides a quasi-best low-rank approximation of high-dimensional data in the hierarchical Tucker framework. Similar to the SVD for matrices, it provides a fundamental but expensive tool for tensor computations. In the present work, we examine generalizations of randomized matrix decomposition methods to higher-order tensors in the framework of the hierarchical tensor representation. In particular we present and analyze a randomized algorithm for the calculation of the hierarchical SVD (HSVD) for the tensor train (TT) format.
CITATION STYLE
Huber, B., Schneider, R., & Wolf, S. (2017). A randomized tensor train singular value decomposition. In Applied and Numerical Harmonic Analysis (pp. 261–290). Springer International Publishing. https://doi.org/10.1007/978-3-319-69802-1_9
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