Tensor-based methods for numerical homogenization from high-resolution images

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A literature survey of low‐rank tensor approximation techniques (2013, neutral): “…• computational tasks in micromagnetics [80,81]; • rational approximation problems [242]; • computational homogenization [42,96,176]; • computational ﬁnance [134,137]; • the approximation of stationary states of stochastic automata networks [38]; • multivariate regression…”
Approximation rates for the hierarchical tensor format in periodic Sobolev spaces (2014, methodology): “In [13] the recent developments have been applied to numerical homogenization.”
Low-rank methods for high-dimensional approximation and model order reduction (2015, unknown): “ (1) m ⊗ ...⊗ U (d) m , with U (ν) m ⊂ U (ν) m+1, therefore allowing a notion of decomposition to be recovered. Construction of subspaces based on rank-one corrections. A ﬁrst strategy, introduced in [42], consists in progressively enriching the spaces by the factors of rank-one corrections. More pr”