Equations for Lower Bounds on Border Rank

DOI10.1080/10586458.2013.825892zbMath1361.68098arXiv1305.0779OpenAlexW2066723539WikidataQ57425375 ScholiaQ57425375MaRDI QIDQ5415563

Christian Ikenmeyer, Jonathan D. Hauenstein, Joseph M. Landsberg

Publication date: 13 May 2014

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1305.0779

zbMATH Keywords

matrix multiplicationborder rank

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Determinantal varieties (14M12) Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) (68Q17)

Related Items (12)

Equations for GL invariant families of polynomials ⋮ A note on the gap between rank and border rank ⋮ Tensor decomposition and homotopy continuation ⋮ Algebraic geometry and representation theory in the study of matrix multiplication complexity and other problems in theoretical computer science ⋮ On the Geometry of Border Rank Decompositions for Matrix Multiplication and Other Tensors with Symmetry ⋮ 16,051 formulas for Ottaviani's invariant of cubic threefolds ⋮ Decomposing tensors into frames ⋮ Decomposing Solution Sets of Polynomial Systems Using Derivatives ⋮ Computing images of polynomial maps ⋮ On the Geometry of Border Rank Algorithms for n × 2 by 2 × 2 Matrix Multiplication ⋮ Unifying known lower bounds via geometric complexity theory ⋮ The Saxl conjecture and the dominance order

Uses Software

• Bertini

Cites Work

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• Witness sets of projections
• Numerical elimination and moduli space of vacua
• On the ideals of secant varieties of Segre varieties
• Membership tests for images of algebraic sets by linear projections
• Gaussian elimination is not optimal
• New lower bounds for the border rank of matrix multiplication
• The border rank of the multiplication of $2\times 2$ matrices is seven
• Partial and Total Matrix Multiplication
• Symmetric Functions Applied to Decomposing Solution Sets of Polynomial Systems
• Algebraic boundaries of Hilbert’s SOS cones
• Toward a Salmon Conjecture

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