Demmel, Question 1.20

Here are some sample plots. The most sensitive roots seem to be towards the high end, ie, at about 7, at about 15, and at about 512. For the complex example, the most sensitive roots are the largest pair.

• r=(1:10), e=1e-3
• r=(1:10), e=1e-7
• r=(1:20), e=1e-11
• r=[2,4,8,...,1024], e=1e-2
• r=[1+j,1-j,3+2j,3-2j,6+j,6-j], e=1e-3