An adaptive algebraic multigrid algorithm for low-rank canonical tensor\n decomposition

2011/11/25 by Hans De Sterck, De Sterck, Hans, Killian Miller +1
Mathematics · Engineering · Computer Science · #Tensor decomposition and applications #Elasticity and Material Modeling #Computational Physics and Python Applications

paper · pdf · doi:10.48550/arxiv.1111.6091

Abstract

This paper presents a multigrid algorithm for the computation of the rank-R\ncanonical decomposition of a tensor for low rank R. Standard alternating least\nsquares (ALS) is used as the relaxation method. Transfer operators and\ncoarse-level tensors are constructed in an adaptive setup phase based on\nmultiplicative correction and on Bootstrap algebraic multigrid. An accurate\nsolution is then computed by an additive solve phase based on the Full\nApproximation Scheme. Numerical tests show that for certain test problems the\nmultilevel method significantly outperforms standalone ALS when a high level of\naccuracy is required.\n

Citations

• Analysis of Individual Differences in Multidimensional Scaling Via an N-way Generalization of “Eckart-Young” Decomposition
• Tensor Decompositions and Applications

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