An Adaptive Algebraic Multigrid Algorithm for Low-Rank Canonical Tensor Decomposition

A new algorithm based on algebraic multigrid is presented for computing the rank-$R$ canonical decomposition of a tensor for small $R$. Standard alternating least squares (ALS) is used as the relaxation method. Transfer operators and coarse-level tensors are constructed in an adaptive setup phase th...

Full description

Saved in:
Bibliographic Details
Published inSIAM journal on scientific computing Vol. 35; no. 1; pp. B1 - B24
Main Authors Sterck, Hans De, Miller, Killian
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.01.2013
Subjects
Algebra
Algorithms
Applied mathematics
Approximation
Computation
Decomposition
Mathematical analysis
Mathematical models
Methods
Optimization
Tensors
Online AccessGet full text
ISSN1064-8275
1095-7197
DOI10.1137/110855934

Cover

More Information
Summary:A new algorithm based on algebraic multigrid is presented for computing the rank-$R$ canonical decomposition of a tensor for small $R$. Standard alternating least squares (ALS) is used as the relaxation method. Transfer operators and coarse-level tensors are constructed in an adaptive setup phase that combines multiplicative correction and bootstrap algebraic multigrid. An accurate solution is computed by an additive solve phase based on the full approximation scheme. Numerical tests show that for certain test problems our multilevel method significantly outperforms standalone ALS when a high level of accuracy is required. [PUBLICATION ABSTRACT]
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ObjectType-Article-2
ObjectType-Feature-1
content type line 23
ISSN:1064-8275
1095-7197
DOI:10.1137/110855934