(a)A``Gaussianizes'' b. y=\sum_k=1^N exp(-(5*(I-j)/N)^2)/N \delta_{jk}=exp(-5((I-k)/N)^2). prob1.m prob1b.fig (b)\lambda_1 varies dramatically around 0, whereas \lambda_N remains relatively stable as N increases. records.txt ev5.fig ev10.fig ev20.fig ev30.fig ev40.fig ev50.fig (c)||x||/||b|| blows up in a similar way as \lambda_N/\lambda_1 does as N increases. records.txt prob1solnx.fig (d)||Ax-b|| increases as N increases due to round-off errors perhaps. records.txt (e)Using A-I, ||x||/||b|| seems to remain stable. I guess the errors in Ax and in Ix cancel out each other. records.txt

Note: I had better understanding after the class on Thursday but those were my original thoughts.

Prob 2 (help from Prof. Barnett) prob2.m dipole.m prob2dipole.fig

Prob 3 prob3.m fordipole.f prob3N20.fig I ran out of time... sorry!