Fast matrix multiplication is stable

Numerische Mathematik

Volumn 106, Issue 2, 2007, Pages 199-224

  Demmel, James ^a,b   Dumitriu, Ioana ^a   Holtz, Olga ^a   Kleinberg, Robert ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34248224610     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00211-007-0061-6     Document Type: Article

References (19)

1. Anderson, E., Bai, Z., Bischof, C., Demmel, J., Dongarra, J., Du Croz, J., Greenbaum, A., Hammarling, S., McKenney, A., Blackford, S., Sorensen, D.: LAPACK Users' Guide, 3rd edn. SIAM, Philadelphia (1999)
2. Bini, D., Lotti, D.: Stability of fast algorithms for matrix multiplication. Numer. Math. 36, 63-72 (1980)
3. Blackford, L.S., Choi, J., Cleary, A., D'Azevedo, E., Deramel, J., Dhillon, I., Dongarra, J., Hammarling, S., Henry, G., Petitet, A., Stanley, K., Walker, D., Whaley, R.C.: ScaLAPACK Users' Guide. SIAM, Philadelphia (1997)
4. Brent, R.P.: Algorithms for matrix multiplication. Report CS 157, Computer Science Department, Stanford University (1970)
5. Brockett, R.W., Dobkin, D.: On the optimal evaluation of a set of bilinear forms. Linear Algebra Appl. 19(3), 207-235 (1978)
6. Bürgisser, P., Clausen, M., Shokrollahi, M.A.: Algebraic complexity theory. In: Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 315. Springer, Berlin (1997)
7. Cohn, H., Kleinberg, R., Szegedy, B., Umans, C.: Group-theoretic algorithms for matrix multiplication. In: Foundations of Computer Science. 46th Annual IEEE Symposium, 23-25 October 2005, pp. 379-388 (2005)
8. Cohn, H., Kleinberg, R., Szegedy, B., Umans, C.: Implementing group-theoretic algorithms for matrix multiplication using the abelian discrete Fourier transform (in preparation)
9. Cohn, H., Umans, C.: A group-theoretic approach to matrix multiplication. In: Foundations of Computer Science. 44th Annual IEEE Symposium, pp. 438-449 (2003)
10. Coppersmith, D., Winograd, S.: Matrix multiplication via arithmetic progressions. J. Symbolic Comput. 9(3), 251-280 (1990)
11. Demmel, J., Dumitriu, I., Holtz, O.: Fast linear algebra is stable (2006, in preparation)
12. Demmel, J., Higham, N.J.: Stability of block algorithms with fast level 3 BLAS. ACM Trans. Math. Soft. 18, 274-291 (1992)
13. Higham, N.J.: Exploiting fast matrix multiplication within the level 3 BLAS. ACM Trans. Math. Soft. 16, 352-368 (1990)
14. Higham, N.J.: Accuracy and Stability of Numerical Algorithms, 2nd edn. SIAM. Philadelphia (2002)
15. Maslen, D.K., Rockmore, D.N.: The Cooley-Tukey FFT and group theory. Not. Am. Math. Soc. 48(10), 1151-1160 (2001)
16. Miller, W.: Computational complexity and numerical stability. SIAM J. Comput. 4(2), 97-107 (1975)
17. Raz, R.: On the complexity of matrix product. SIAM J. Comput. 32(5), 1356-1369 (electronic) (2003)
18. Schönhage, A., Strassen, V.: Schnelle Multiplikation grosser Zahlen. Computing (Arch. Elektron. Rechnen) 7, 281-292 (1971)
19. Strassen, V.: Gaussian elimination is not optimal. Numer. Math. 13, 354-356 (1969)