Low-Rank Matrix and Tensor Approximation

Low-rank matrix and tensor approximation has become an ubiquitous technique for dealing with the computational challenges incurred by high-dimensional data and functions. This tutorial will cover key algorithms and results concerning low-rank approximation. This includes insights on the question when low-rank approximation can be expected to work well (and when not) and the choice of algorithm based on how a given matrix or tensor is accessed. Numerous applications and examples how low-rank approximation is used in statistical learning, model reduction, uncertainty quantification, simulation of quantum systems, etc. will be provided.

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