NDLI: Two-Level QTT-Tucker Format for Optimized Tensor Calculus

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Khoromskij, Boris Dolgov, Sergey
Copyright Year	2013
Abstract	We propose a combined tensor format, which encapsulates the benefits of Tucker, tensor train (TT), and quantized TT (QTT) formats. The structure is composed of subtensors in TT representations, so the approximation problem is proven to be stable. We describe all important algebraic and optimization operations, which are recast to the TT routines. Several examples on explicit function and operator representations are provided. The asymptotic storage complexity is at most cubic in the rank parameter, that is larger than for the global QTT approximation, but the numerical examples manifest that the ranks in the two-level format usually increase more slowly with the approximation accuracy than the QTT ones. In particular, we observe that high rank peaks, which usually occur in the TT/QTT representations, are significantly relaxed. Thus the reduced costs can be achieved.
Starting Page	593
Ending Page	623
Page Count	31
File Format	PDF
ISSN	08954798
DOI	10.1137/120882597
e-ISSN	10957162
Journal	SIAM Journal on Matrix Analysis and Applications (SJMAEL)
Issue Number	2
Volume Number	34
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2013-05-16
Access Restriction	Subscribed
Subject Keyword	Multilinear algebra, tensor products tensor methods multilinear algebra constructive tensor representations DMRG/ALS Sparse matrices tensor formats Numerical approximation and evaluation higher dimensions Solution of discretized equations Spectral, collocation and related methods Other matrix algorithms Iterative methods for linear systems QTT format Tucker format
Content Type	Text
Resource Type	Article
Subject	Analysis

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