Thursday, 7 June 2007

na.numerical analysis - Can we find an l-2 sequence if we know all l-p norms?

Sorry to answer my own question, but having thought about it more, I realize this is impossible unless you have arbitrarily high precision for all the |c|p|c|p's. The reason is, as pp grows, the leading digits of |c|pp|c|pp will mainly be those of ck1ck1.



If one does have arbitrary precision, take c1=|c|infty=lim|c|pc1=|c|infty=lim|c|p. To compute this, increase pp until you have "enough" significant digits. Then to get c2c2, subtract cp1cp1 from all the |c|pp|c|pp's and repeat to get c2c2, and so on.



Obviously, your estimate of ckck will be worse than that of ck1ck1, and in double precision I wasn't able to get more than 2 or 3 terms (depends on how large/small the ratios ck1/ckck1/ck are).

No comments:

Post a Comment