to a higher power, the improvement also shrinks geometrically” Is there a proof for this? ]]>

1) Do not get me wrong. I like the work by Andrew and Virginia.

Both are great pieces of hard work.

But if you know the work by Coppersmith and Winograd (and from

what I read in other comments/posts, not many people do), then

you know the limitations of their methods before reading their papers. I do not have a formal lower bound of what you can get

out of the outer structure of the Coppersmith and Winograd

tensor, but from what one typically observes, the improvement

shrinks geometrically with the power you take.

2) One possible reason why you do

not get anything from the third power is that it is the product

of the second and the first power. The second power is

superior to the first power. Note that taking the second,

fourth or whatever power is done for the sake of analysis.

In the construction, you take a huge power of the tensor.

And then it is better to think of it as a product of

second powers of the tensor than of a product of

second powers as well as first powers. (Again, I cannot

prove this.)

3) Ian Gordon, the internal examiner, and myself told

Andrew after his viva to put a preprint online as soon

as possible. Read the update in the post why he did not.

4) “The calculations in Stother’s paper are correct” in my

comment means that they are not wrong.

Some comments before raised the question whether there

was a serious flaw in Stother’s work. It is not.