Lower bounds for the multiplicative complexity of matrix multiplication

Computational Complexity

Volumn 8, Issue 3, 1999, Pages 203-226

  Bläser, Markus ^a  

^a UNIVERSITY OF BONN   (Germany)

Author keywords

Lower bound; Matrix multiplication; Multiplicative complexity; Substitution method

Indexed keywords

EID: 0040531570     PISSN: 10163328     EISSN: None     Source Type: Journal    
DOI: 10.1007/s000370050028     Document Type: Article

References (13)

1. A. ALDER AND V. STRASSEN, On the algorithmic complexity of associative algebras, Theoret. Comput. Sci. 15 (1981), 201-211.
2. R. W. BROCKETT AND D. DOBKIN, On the optimal evaluation of a set of bilinear forms, Linear Algebra and Appl. 19 (1978), 207-235.
3. P. BÜRGISSER, M. CLAUSEN, AND M. A. SHOKROLLAHI, Algebraic Complexity Theory, Springer-Verlag, 1997.
4. H. F. DE GROOTE, On the varieties of optimal algorithms for the computation of bilinear mappings: The isotropy group of a bilinear mapping, Theoret. Comput. Sci. 7 (1978), 1-24.
5. H. F. DE GROOTE, Lectures on the Complexity of Bilinear Problems, LNCS 245, Springer-Verlag, 1986.
6. J. HOPCROFT AND L. KERR, On minimizing the number of multiplications necessary for matrix multiplication, SIAM J. Appl. Math. 20 (1971), 20-36.
7. J. JA'JA', On the complexity of bilinear forms with commutativity, SIAM J. Comput. 9 (1980), 717-738.
8. J. C. LAFON AND S. WINOGRAD, A lower bound for the multiplicative complexity of the product of two matrices, Centre de Calcul de L'Esplanade, U.E.R. de Mathématique, Univ. Louis Pasteur, Strasbourg, France, 1978.
9. V. PAN, Methods for computing values of polynomials, Russ. Math. Surv. 21 (1966), 105-136.
10. I. R. SHAFAREVICH, Basic Algebraic Geometry, Springer-Verlag, 1974.
11. V. STRASSEN, Gaussian elimination is not optimal, Num. Math. 13 (1969), 354-356.
12. V. STRASSEN, Vermeidung von Divisionen, J. Reine Angew. Math. 264 (1973), 184-202.
13. V. STRASSEN, Algebraic complexity theory, in Handbook of Theoretical Computer Science Vol. A, J. van Leeuven, ed., Elsevier Science Publishers B.V., 1990, 634-672.