A regularized Newton method for the efficient approximation of tensors represented in the canonical tensor format

DOI10.1007/s00211-012-0465-9zbMath1264.65087OpenAlexW2071529930MaRDI QIDQ1938432

Mike Espig, Wolfgang Hackbusch

Publication date: 4 February 2013

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-012-0465-9

zbMATH Keywords

algorithmnumerical experimentsminimization methodregularized Newton methodlow tensor rank approximationpre-Hilbert tensor product spaces

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Large-scale problems in mathematical programming (90C06) Nonconvex programming, global optimization (90C26) Methods of quasi-Newton type (90C53) Multilinear algebra, tensor calculus (15A69)

Related Items (15)

Mesh-free canonical tensor products for six-dimensional density matrix: computation of kinetic energy ⋮ Numerical tensor techniques for multidimensional convolution products ⋮ The Optimization Landscape for Fitting a Rank-2 Tensor with a Rank-1 Tensor ⋮ Efficient low-rank approximation of the stochastic Galerkin matrix in tensor formats ⋮ Numerical Approximation of PGD Modes to Parameterized Elliptic Problems ⋮ Rank properties and computational methods for orthogonal tensor decompositions ⋮ Variational calculus with sums of elementary tensors of fixed rank ⋮ The numerical approximation of nonlinear functionals and functional differential equations ⋮ Parallel tensor methods for high-dimensional linear PDEs ⋮ Algorithm 941 ⋮ Numerical tensor calculus ⋮ The Dynamics of Swamps in the Canonical Tensor Approximation Problem ⋮ Iterative algorithms for the post-processing of high-dimensional data ⋮ Tensor Spaces and Hierarchical Tensor Representations ⋮ A literature survey of low-rank tensor approximation techniques

Uses Software

• Multilinear Engine

Cites Work

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• Approximate iterations for structured matrices
• Rank-One Approximation to High Order Tensors
• Numerical operator calculus in higher dimensions
• Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem
• Multilinear Algebra
• Algorithms for Numerical Analysis in High Dimensions
• Approximation of 1/x by exponential sums in [1, ∞)

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