On norm compression inequalities for partitioned block tensors

DOI10.1007/s10092-020-0356-xzbMath1436.15027OpenAlexW3006445651WikidataQ114228541 ScholiaQ114228541MaRDI QIDQ2174201

Zhening Li, Yun-bin Zhao

Publication date: 21 April 2020

Published in: Calcolo (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10092-020-0356-x

zbMATH Keywords

spectral normrank-one approximationblock tensornorm compression inequalitytensor partition

Mathematics Subject Classification ID

Approximation methods and heuristics in mathematical programming (90C59) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Miscellaneous inequalities involving matrices (15A45) Multilinear algebra, tensor calculus (15A69) Numerical methods for low-rank matrix approximation; matrix compression (65F55)

Related Items (4)

Extreme Ratio Between Spectral and Frobenius Norms of Nonnegative Tensors ⋮ Maximum relative distance between real rank-two and rank-one tensors ⋮ Chebyshev Polynomials and Best Rank-one Approximation Ratio ⋮ On the tensor spectral \(p\)-norm and its dual norm via partitions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Tensor Decompositions and Applications
• On the nuclear norm and the singular value decomposition of tensors
• Approximation algorithms for discrete polynomial optimization
• Operator norm inequalities between tensor unfoldings on the partition lattice
• Approximation algorithms for homogeneous polynomial optimization with quadratic constraints
• Deterministic approximation algorithms for sphere constrained homogeneous polynomial optimization problems
• A norm compression inequality for block partitioned positive semidefinite matrices
• Hierarchical matrices. A means to efficiently solve elliptic boundary value problems
• Norm inequalities for partitioned operators and an application
• Inequalities for trace norms of \(2\times 2\) block matrices.
• New trace norm inequalities for \(2\times 2\) blocks of diagonal matrices
• Block tensors and symmetric embeddings
• Adaptive covariance matrix estimation through block thresholding
• Equivalence constants for matrix norms: A problem of Goldberg
• On the tensor spectral \(p\)-norm and its dual norm via partitions
• Tensor principal component analysis via convex optimization
• Relations of the nuclear norm of a tensor and its matrix flattenings
• Combinatorial methods for the spectral \(p\)-norm of hypermatrices
• On a norm compression inequality for \(2\times N\) partitioned block matrices
• Bounds on the Spectral Norm and the Nuclear Norm of a Tensor Based on Tensor Partitions
• Maximum Block Improvement and Polynomial Optimization
• Block Tensor Unfoldings
• Semidefinite Relaxations for Best Rank-1 Tensor Approximations
• The Best Rank-One Approximation Ratio of a Tensor Space
• Estimating the Largest Eigenvalue by the Power and Lanczos Algorithms with a Random Start
• Nuclear norm of higher-order tensors
• Quantum information theory
• The Best Rank-1 Approximation of a Symmetric Tensor and Related Spherical Optimization Problems
• Chebyshev Polynomials and Best Rank-one Approximation Ratio
• A Unifying Perron--Frobenius Theorem for Nonnegative Tensors via Multihomogeneous Maps
• Probability Bounds for Polynomial Functions in Random Variables
• Hardness and Approximation Results for L_p-Ball Constrained Homogeneous Polynomial Optimization Problems
• Computing the Gradient in Optimization Algorithms for the CP Decomposition in Constant Memory through Tensor Blocking
• Blind Multilinear Identification
• On Orthogonal Tensors and Best Rank-One Approximation Ratio
• Approximation Methods for Polynomial Optimization
• Most Tensor Problems Are NP-Hard

This page was built for publication: On norm compression inequalities for partitioned block tensors