The basic idea of reducing 4 multiplications to 3 multiplications (ax + b)(cx + d) = acx^2 + [(a + b)(c + d) - ac - bd]x + bd holds pretty generally; there is

The basic idea of reducing 4 multiplications to 3 multiplications (ax + b)(cx + d) = acx^2 + [(a + b)(c + d) - ac - bd]x + bd holds pretty generally; there isn't any new math or algorithm here that I can see. Their own complexity analysis (eqns. 7 and 8) shows this performs about the same as using Karatsuba multiplication on the entries of the matrices (instead of on the matrices themselves).