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Greenk12 2008-11-15 09:42

About random number (random seed) in Msieve

I have question about Block Lanczos algorithm (Montgomery) :

As i know during run Block Lanczos algorithm - we select random a matrix Y (size nxN, N = 64), therefore we use this matrix to run Block Lanczos algorithm. So i want to ask:

Can we know matrix Y that we initialized is best to run Block Lanczos algorithm? (I mean: if we use matrix Y, we always run Block Lanczos algorithm success.) And oppose, can we know matrix Y is bad to run Block Lanczos algorithm? (if we use bad matrix Y, Block Lanczos algorithm can fail!).

Thank for your reading.

jasonp 2008-11-15 13:56

Block Lanczos only works with high probability, and the most that anyone has proved is that failure is extremely rare when the initial vector is chosen randomly. There is no way to tell when failure will happen, otherwise proving convergence would not be an interesting problem :)

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