Three decompositions of symmetric tensors have similar condition numbers

DOI10.1016/j.laa.2023.01.020OpenAlexW3205634189MaRDI QIDQ2689155

Nick Vannieuwenhoven, Paul Breiding, Nick Dewaele

Publication date: 9 March 2023

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2110.04172

zbMATH Keywords

condition numbercanonical polyadic decompositionWaring decomposition

Mathematics Subject Classification ID

Numerical computation of matrix norms, conditioning, scaling (65F35) Multilinear algebra, tensor calculus (15A69) Local Riemannian geometry (53B20) Computational aspects in algebraic geometry (14Qxx) Sensitivity analysis for optimization problems on manifolds (49Q12)

Uses Software

• Julia

Cites Work

• Remarks on the Symmetric Rank of Symmetric Tensors
• Tensor decompositions for learning latent variable models
• Julia: A Fresh Approach to Numerical Computing
• A Multilinear Singular Value Decomposition
• A Counterexample to Comon's Conjecture
• The Condition Number of Join Decompositions
• Minimality and uniqueness for decompositions of specific ternary forms
• The Structured Condition Number of a Differentiable Map between Matrix Manifolds, with Applications
• Symmetric Tensors and Symmetric Tensor Rank
• Effective Criteria for Specific Identifiability of Tensors and Forms
• A Theory of Condition
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