There is an ironic tension with these. Using the power iterations is generally bad numerically, but having a small p is much worse for accuracy. That means that factoring (A' A)^q A will get much more accurate values for the same value of p. Alternately phrased, getting the same accuracy would require a much larger value of p and thus would overcome the cost of the initial power iteration.
How this works out in practice on truly massive scale is totally up in the air. The result of the stochastic projection can actually be *larger* than the original sparse matrix which would seem to imply that the power method might actually save time sometimes. On Thu, Nov 18, 2010 at 11:07 AM, Dmitriy Lyubimov <[email protected]>wrote: > Further work on this may include implementation of power iterations > (although i doubt there's much to be had of them on such big volumes). >
