http://math.cityu.edu.hk/~mayylu/ma6606/6606.pdf
p34. Q6
Consider the Cholesky decomposition of a 2 2 real symmetric positive denite matrix
A =
[a b
b c]
= SST =
pa
b=pa
p
c b2=a
pa b=pa p
c b2=a
:
Let sij be the (i; j) entry of S, we use the following algorithm to calculate S:
s11 = pa; s21 = b=s11; s22 =
q
c s2
21:
Show that this algorithm is backward stable. Namely, the computer result (using
oating
point operations) S~ satises S~S~T = A~ for some A~ close to A.