New Lower Bounds for the Rank of Matrix Multiplication
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Publication:5419033
DOI10.1137/120880276zbMath1298.68100arXiv1206.1530OpenAlexW2964247109MaRDI QIDQ5419033
Publication date: 4 June 2014
Published in: SIAM Journal on Computing (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1206.1530
Analysis of algorithms and problem complexity (68Q25) Computational aspects and applications of commutative rings (13P99) Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) (68Q17) Effectivity, complexity and computational aspects of algebraic geometry (14Q20)
Related Items (15)
Universal points in the asymptotic spectrum of tensors ⋮ On the nuclear norm and the singular value decomposition of tensors ⋮ New applications of the polynomial method: The cap set conjecture and beyond ⋮ Abelian tensors ⋮ An introduction to the computational complexity of matrix multiplication ⋮ The rank of \(n \times n\) matrix multiplication is at least \(3n^2 - 2\sqrt{2}n^{\frac{3}{2}} - 3n\) ⋮ On the Geometry of Border Rank Decompositions for Matrix Multiplication and Other Tensors with Symmetry ⋮ On bilinear complexity of multiplying \(2 \times 2\)-matrix by \(2 \times m\)-matrix over finite field ⋮ Fast matrix multiplication and its algebraic neighbourhood ⋮ Corrigendum to ``The rank of \(n{\times}n\) matrix multiplication is at least \(3n^2 - 2\sqrt{2}n^{\frac{3}{2}} - 3n\) ⋮ Lower bound for ranks of invariant forms ⋮ On non-commutative rank and tensor rank ⋮ Improving the Numerical Stability of Fast Matrix Multiplication ⋮ Nontriviality of equations and explicit tensors in \(\mathbb{C}^m \otimes \mathbb{C}^m \otimes \mathbb{C}^m\) of border rank at least \(2m - 2\) ⋮ Unifying known lower bounds via geometric complexity theory
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