Spectral norm of a symmetric tensor and its computation

DOI10.1090/mcom/3525zbMath1452.15013arXiv1808.03864OpenAlexW3023388044MaRDI QIDQ5113665

Li Wang, Shmuel Friedland

Publication date: 15 June 2020

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1808.03864

zbMATH Keywords

symmetric tensorsentanglementhomogeneous polynomialsspectral norm\(d\)-mode symmetric qubits\(d\)-mode symmetric qunitsanti-fixed and fixed pointscomputation of spectral norm

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Eigenvalues, singular values, and eigenvectors (15A18) Multilinear algebra, tensor calculus (15A69) Quantum coherence, entanglement, quantum correlations (81P40) Numerical computation of roots of polynomial equations (65H04) Solving polynomial systems; resultants (13P15)

Related Items

On the complexity of finding tensor ranks ⋮ Spectral inequalities for nonnegative tensors and their tropical analogues ⋮ Large-sample properties of unsupervised estimation of the linear discriminant using projection pursuit ⋮ The Relation Between a Tensor and Its Associated Semi-Symmetric Form

Uses Software

• Bertini
• ISOLATE

Cites Work

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• The number of singular vector tuples and uniqueness of best rank-one approximation of tensors
• Definability and fast quantifier elimination in algebraically closed fields
• Solving zero-dimensional systems through the rational univariate representation
• Efficient computation of zero-dimensional Gröbner bases by change of ordering
• How entangled can two couples get?
• The tensor rank of tensor product of two three-qubit W states is eight
• The number of eigenvalues of a tensor
• Best rank one approximation of real symmetric tensors can be chosen symmetric
• On the complexity of the \(F_5\) Gröbner basis algorithm
• An efficient algorithm for the complex roots problem
• Rank-One Approximation to High Order Tensors
• Maximum Block Improvement and Polynomial Optimization
• Semidefinite Relaxations for Best Rank-1 Tensor Approximations
• On best rank one approximation of tensors
• Multicorns are not Path Connected
• Low-Rank Approximation of Tensors
• Sums of even powers of real linear forms
• Estimating the Largest Eigenvalue by the Power and Lanczos Algorithms with a Random Start
• On the Best Rank-1 and Rank-(R₁ ,R₂ ,. . .,R_N) Approximation of Higher-Order Tensors
• Nuclear norm of higher-order tensors
• Most boson quantum states are almost maximally entangled
• Computation of the geometric measure of entanglement for pure multiqubit states
• Random Matrices and Complexity of Spin Glasses
• Reducibility among Combinatorial Problems
• Sparse Rational Univariate Representation
• The maximally entangled symmetric state in terms of the geometric measure
• Efficient computation of the characteristic polynomial
• Maxima for Graphs and a New Proof of a Theorem of Turán
• Most Tensor Problems Are NP-Hard
• Geometry of Quantum States
• Matrices
• Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?
• Über homogene Polynome in ($L^{2}$)
• Unique Arrangements of Points on a Sphere
• Coherence in Spontaneous Radiation Processes
• Inverse eigenvalue problems