  We perform forward error analysis for a large class of recursive matrix
multiplication algorithms in the spirit of [D. Bini and G. Lotti, Stability of
fast algorithms for matrix multiplication, Numer. Math. 36 (1980), 63--72]. 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 [H.
Cohn, and C. Umans, A group-theoretic approach to fast matrix multiplication,
FOCS 2003, 438--449] and [H. Cohn, R. Kleinberg, B. Szegedy and C. Umans,
Group-theoretic algorithms for matrix multiplication, FOCS 2005, 379--388] 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.
