http://math.cityu.edu.hk/~mayylu/ma6606/6606.pdf
p34. Q6

Consider the Cholesky decomposition of a 2  2 real symmetric positive de nite 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~ satis es S~S~T = A~ for some A~ close to A.