Lectures on the complexity of bilinear problems

zbMath0609.68032MaRDI QIDQ1087014

Hans F. de Groote

Publication date: 1987

Published in: Lecture Notes in Computer Science (Search for Journal in Brave)

zbMATH Keywords

algebras of minimal rankvarietyalgebraic complexitytensor ranktensorsbilinear algorithmsmatrix multiplicationbilinear mappingsborder rankmultiplication of polynomialsmultiplication in algebrasmultiplication tensor

Mathematics Subject Classification ID

Analysis of algorithms and problem complexity (68Q25) Symbolic computation and algebraic computation (68W30) Endomorphism rings; matrix rings (16S50) Vector and tensor algebra, theory of invariants (15A72) Research exposition (monographs, survey articles) pertaining to computer science (68-02) Research exposition (monographs, survey articles) pertaining to linear algebra (15-02) Research exposition (monographs, survey articles) pertaining to associative rings and algebras (16-02)

Related Items (18)

Multiplicative complexity of direct sums of quadratic systems ⋮ Maximal bilinear complexity and codes ⋮ Semi-algebraic complexity -- Additive complexity of matrix computational tasks ⋮ Bilinear mincing rank ⋮ Communication complexity of multi-processor systems ⋮ On the order of approximation in approximative triadic decompositions of tensors ⋮ On the complexity of the multiplication of matrices of small formats ⋮ The complexity of bivariate power series arithmetic. ⋮ Bilinear complexity of algebras and the Chudnovsky-Chudnovsky interpolation method ⋮ An optimal algorithm for multiplication in \(\mathbb{F}_{256}/\mathbb{F}_ 4\) ⋮ Multilinear algebra and parallel programming ⋮ On the rank of certain finite fields ⋮ Efficient randomized generation of optimal algorithms for multiplication in certain finite fields ⋮ Beyond the Alder-Strassen bound. ⋮ Improved method for finding optimal formulas for bilinear maps in a finite field ⋮ The border rank of the multiplication of $2\times 2$ matrices is seven ⋮ On the direct sum conjecture in the straight line model ⋮ On a class of primary algebras of minimal rank

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