Fast matrix multiplication is stable |
| |
Authors: | James Demmel Ioana Dumitriu Olga Holtz Robert Kleinberg |
| |
Institution: | (1) Mathematics Department, University of California, Berkeley, CA 94720, USA;(2) Computer Science Division, University of California, Berkeley, CA 94720, USA |
| |
Abstract: | We perform forward error analysis for a large class of recursive matrix multiplication algorithms in the spirit of Bini and
Lotti Numer. Math. 36:63–72, 1980]. As a consequence of our analysis, we show that the exponent of matrix multiplication
(the optimal running time) can be achieved by numerically stable algorithms. We also show that new group-theoretic algorithms
proposed in Cohn and Umans Foundations of Computer Science, 44th Annual IEEE Symposium, pp. 438–449, 2003] and Cohn et al.
Foundations of Computer Science, 46th Annual IEEE Symposium, pp. 379–388, 2005] are all included in the class of algorithms
to which our analysis applies, and are therefore numerically stable. We perform detailed error analysis for three specific
fast group-theoretic algorithms.
J. Demmel acknowledges support of NSF under grants CCF-0444486, ACI-00090127, CNS-0325873 and of DOE under grant DE-FC02-01ER25478.
I. Dumitriu acknowledges support of the Miller Institute for Basic Research in Science.
R. Kleinberg is supported by an NSF Mathematical Sciences Postdoctoral Research Fellowship |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|