Geometry and the complexity of matrix multiplication
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Publication:3498865
DOI10.1090/S0273-0979-08-01176-2zbMath1145.68054MaRDI QIDQ3498865
Publication date: 19 May 2008
Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)
Analysis of algorithms and problem complexity (68Q25) Symbolic computation and algebraic computation (68W30) Computational aspects of higher-dimensional varieties (14Q15) Multilinear algebra, tensor calculus (15A69)
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Cites Work
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- A note on border rank
- Matrix multiplication via arithmetic progressions
- Rank and optimal computation of generic tensors
- Typical tensorial rank
- Invariants of phylogenies in a simple case with discrete states
- On the algorithmic complexity of associative algebras
- On the optimal evaluation of a set of bilinear forms
- \(0(n^{2.7799})\) complexity for \(n\times n\) approximate matrix multiplication
- On the complexity of the multiplication of matrices of small formats
- On the projective geometry of rational homogeneous varieties
- Phylogenetic invariants for the general Markov model of sequence mutation
- On the ideals of secant varieties of Segre varieties
- Ranks of tensors, secant varieties of Segre varieties and fat points
- On the ideals of secant varieties to certain rational varieties
- Algebraic geometry of Bayesian networks
- Phylogenetic ideals and varieties for the general Markov model
- On the Alexander-Hirschowitz theorem
- Quivers and the cohomology of homogeneous vector bundles
- Gaussian elimination is not optimal
- On multiplication of 2 \(\times\) 2 matrices
- The border rank of the multiplication of $2\times 2$ matrices is seven
- On the ideals and singularities of secant varieties of Segre varieties
- Induction for secant varieties of Segre varieties
- On the complexity of some algorithms of matrix multiplication
- Relative bilinear complexity and matrix multiplication.
- Partial and Total Matrix Multiplication
- Varieties of small codimension in projective space
- A noncommutative algorithm for multiplying 3×3 matrices using 23 multiplications
- Secant varieties of Grassmann varieties
- Prolongations and Computational Algebra
- Geometry and Complexity Theory
- Generalizations of Strassen's Equations for Secant Varieties of Segre Varieties
- Geometry of Quantum States
- On Winograd's Algorithm for Inner Products
- On Minimizing the Number of Multiplications Necessary for Matrix Multiplication
- Algebraic Statistics for Computational Biology
