2014 · 209 citations · 16 references
ComputingComputer ScienceMathematicsAlgebraOptimizationTheory Of ComputationAlgorithm AnalysisComplexity TheoryComputational AlgebraComputational ComplexityMatrix ComputationTime ComplexityAsymptotic AnalysisComplexity Of Numerical AlgorithmsMatrix ExponentiationMatrix MultiplicationPolynomial Time ComplexityPolynomial-time AlgorithmsSymbolic ComputationUpper Bounds
This tutorial will give an overview of algebraic complexity theory focused on bilinear complexity, and describe several powerful techniques to analyze the complexity of computational problems from linear algebra, in particular matrix multiplication. The presentation of these techniques will follow the history of progress on constructing asymptotically fast algorithms for matrix multiplication, and include its most recent developments.
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Gaussian elimination is not optimal
Volker Strassen · Numerische Mathematik · 1969 · 2.5K citations
Matrix multiplication via arithmetic progressions
Don Coppersmith, S. Winograd · Journal of Symbolic Computation · 1990 · 2.3K citations
Multiplying matrices faster than coppersmith-winograd
Virginia Vassilevska Williams · 2012 · 887 citations
Powers of tensors and fast matrix multiplication
François Le Gall · 2014 · 873 citations
Gaussian Elimination is not Optimal
Volker Trassen · 2005 · 460 citations