Variational calculus with sums of elementary tensors of fixed rank

By M. Espig, Wolfgang Hackbusch, Thorsten Rohwedder, Reinhold Schneider. 2012

16 citations recorded by the source corpus.

Subfields: Computational Mathematics, Computational Theory and Mathematics

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Citations in the corpus

A literature survey of low‐rank tensor approximation techniques (2013, neutral): “For tensors in CP decomposition, the approximate solution of (8) by gradient techniques has been discussed in [79].”
On Local Convergence of Alternating Schemes for Optimization of Convex Problems in the Tensor Train Format (2013, background): “Also, for treatment of more complex equations as optimization problems, application of this format is possible [11], but has to be stabilized by somewhat artificial techniques [10]; when it comes to treatment of equations based on a manifold approach [19], CANDECOMP lacks the basic property of being”
LOCAL CONVERGENCE OF ALTERNATING SCHEMES FOR OPTIMIZATION OF CONVEX PROBLEMS IN THE TT FORMAT (2011, background): “Also, for treatment of more complex equations as optimization problems, application of this format is possible [10], but has to be stabilized by somewhat arti cial techniques [9]; when it comes to treatment of equations based on a manifold approach [17], CANDECOMP lacks the basic property of being a”
F ¨ Ur Mathematik in Den Naturwissenschaften Leipzig a Projection Method to Solve Linear Systems in Tensor Format a Projection Method to Solve Linear Systems in Tensor Format (unknown): “Espig, Hackbusch, Rohwedder, and Schneider [7] have proposed a direct minimisation of the functional f (x) = Ax − b 2 where x is assumed to be of fixed rank.”
Algorithm 941 (2014, background): “The second strategy is to reformulate the problem at hand as an optimization problem with the admissible set of solutions restricted to data-sparse tensors, see [8, 16, 17, 22, 29, 30] and the references therein.”