- Main
Fast matrix multiplication is stable
Published Web Location
http://www.springerlink.com/content/w7158p34v2248073/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.
Many UC-authored scholarly publications are freely available on this site because of the UC's open access policies. Let us know how this access is important for you.
Main Content
Enter the password to open this PDF file:
-
-
-
-
-
-
-
-
-
-
-
-
-
-