Beyond the Alder-Strassen bound

Theoretical Computer Science

Volumn 331, Issue 1, 2005, Pages 3-21

  Bläser, Markus ^a,b  

^a UNIVERSITY OF LÜBECK   (Germany)

^b ETH ZURICH   (Switzerland)

Author keywords

Associative algebra; Lower bound; Multiplicative complexity

Indexed keywords

COMPUTATION THEORY; DECOMPOSITION; MATRIX ALGEBRA; POLYNOMIALS; TENSORS;

ALDER-STRASSEN BOUND; ASSOCIATIVE ALGEBRA; LOWER BOUND; MULTIPLICATIVE COMPLEXITY;

COMPUTER SCIENCE;

EID: 15744381973     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tcs.2004.09.029     Document Type: Conference Paper

References (27)

1. A. Alder, and V. Strassen On the algorithmic complexity of associative algebras Theoret. Comput. Sci. 15 1981 201 211
2. D. Bini, M. Capovani, G. Lotti, and F. Romani O (n 2.7799) complexity for matrix multiplication Inform. Proc. Lett. 8 1979 234 235
3. M. Bläser Lower bounds for the multiplicative complexity of matrix multiplication Comput. Complexity 8 1999 203 226
4. M. Bläser A 5 2 n 2 -lower bound for the rank of n × n -matrix multiplication over arbitrary fields Proc. 40th Annu. IEEE Symp. on Foundations of Computer Science (FOCS) 1999 45 50
5. M. Bläser, Untere Schranken für den Rang assoziativer Algebren, Dissertation, Universität Bonn, 1999.
6. M. Bläser Lower bounds for the bilinear complexity of associative algebras Comput. Complexity 9 2000 73 112
7. M. Bläser, A 5 2 n 2 -lower bound for the multiplicative complexity of n × n -matrix multiplication, in: Proc. 18th Internat. GI-MIMD Symp. on Theoretical Aspects of Computer Science (STACS), Lecture Notes in Computer Science, vol. 2010, 2001, pp. 99-110.
8. M. Bläser, Improvements of the Alder-Strassen bound: algebras with nonzero radical, in: Proc. 28th Internat. EATCS Colloquium on Automata, Languages, and Programming (ICALP), Lecture Notes in Computer Science 2076, 2001, pp. 79-91.
9. M. Bläser The complexity of bivariate power series arithmetic Theoret. Comput. Sci. 295 2003 65 83
10. R.W. Brockett, and D. Dobkin On the optimal evaluation of a set of bilinear forms Linear Algebra Appl. 19 1978 207 235
11. N.H. Bshouty A lower bound for matrix multiplication SIAM J. Comput. 18 1989 759 765
12. W. Büchi, Über eine Klasse von Algebren minimalen Rangs, Dissertation, Universität Zürich, 1984.
13. P. Bürgisser, M. Clausen, and M.A. Shokrollahi Algebraic Complexity Theory 1997 Springer Berlin
14. D. Coppersmith, and S. Winograd Matrix multiplication via arithmetic progression J. Symbolic Comput. 9 1990 251 280
15. Y.A. Drozd, and V.V. Kirichenko Finite Dimensional Algebras 1994 Springer Berlin
16. H.F. de Groote Characterization of division algebras of minimal rank and the structure of their algorithm varieties SIAM J. Comput. 12 1983 101 117
17. H.F. de Groote, Lectures on the Complexity of Bilinear Problems, Lecture Notes in Computer Science, vol. 245, Springer, Berlin, 1986.
18. J. Heintz, J. Morgenstern, On associative algebras of minimal rank, in: Proc. Second Applied Algebra and Error Correcting Codes Conference (AAECC), Lecture Notes in Computer Science, vol. 228, Springer, Berlin, 1986, pp. 1-24.
19. J. Ja'Ja' On the complexity of bilinear forms with commutativity SIAM J. Comput. 9 1980 717 738
20. J.-C. Lafon, S. Winograd, A lower bound for the multiplicative complexity of the product of two matrices, Tech. Report, Centre de Calcul de L'Esplanade, U.E.R. de Mathematique, University of Louis Pasteur, Strasbourg, France, 1978.
21. V.Y. Pan Methods for computing values of polynomials Russian Math. Surveys 21 1966 105 136
22. A. Schönhage Partial and total matrix multiplication SIAM J. Comput. 10 1981 434 455
23. A. Shpilka Lower bound for matrix product 42nd Annu. IEEE Symp. on Foundations of Computer Science (FOCS) 2001 358 367
24. V. Strassen Gaussian elimination is not optimal Numer. Math. 13 1969 354 356
25. V. Strassen Vermeidung von Divisionen J. Reine Angew. Math. 264 1973 184 202
26. V. Strassen Rank and optimal computation of generic tensors Linear Algebra Appl. 52/53 1983 645 685
27. V. Strassen Relative bilinear complexity and matrix multiplication J. Reine Angew. Math. 375/376 1987 406 443