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.