Iterative Methods Based on Soft Thresholding of Hierarchical Tensors

Iterative Methods Based on Soft Thresholding of Hierarchical Tensors We construct a soft thresholding operation for rank reduction in hierarchical tensors and subsequently consider its use in iterative thresholding methods, in particular for the solution of discretized high-dimensional elliptic problems. The proposed method for the latter case adjusts the thresholding parameters, by an a posteriori criterion requiring only bounds on the spectrum of the operator, such that the arising tensor ranks of the resulting iterates remain quasi-optimal with respect to the algebraic or exponential-type decay of the hierarchical singular values of the true solution. In addition, we give a modified algorithm using inexactly evaluated residuals that retains these features. The effectiveness of the scheme is demonstrated in numerical experiments. Foundations of Computational Mathematics Springer Journals

Iterative Methods Based on Soft Thresholding of Hierarchical Tensors

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Springer US
Copyright © 2016 by SFoCM
Mathematics; Numerical Analysis; Economics, general; Applications of Mathematics; Linear and Multilinear Algebras, Matrix Theory; Math Applications in Computer Science; Computer Science, general
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