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A continuous analogue of the tensor-train decomposition

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Academic year: 2021

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Table 1: Limitations of grid discretization and tensor-of-coefficients formulations for computing with functions
Figure 1: Hierarchical data structure for storing low-rank functions. Parameters are represented by red squares and functions are represented in blue
Figure 3: Univariate functions for a fixed TT-rank=2 approximation. Marks indicate the location of knots found through adaptive piecewise polynomial procedures
Figure 4: Comparison of convergence for FT (blue), QTT (red), and TT (brown) for the probability density functions of d-dimensional normal random variables
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