Consider the function here A is a symmetric and positive definite 2 × 2 matrix, and v = ( 1 , 2 ) T . The contour plot for F is shown below in Figure 8.32. (a) Also shown in the figure is the starting...

Consider the functionhere A is a symmetric and positive definite 2 × 2 matrix, and
v
= (
₁,

₂)
^T

. The contour plot for F is shown below in Figure 8.32.

(a) Also shown in the figure is the starting point
v
₁
and the point
v
₂
calculated using the CGM. Determine where the next point
v
₃
is located. Make sure to clearly explain how you arrive at your answer.

(b) If one uses the same starting point
v
₁
for the SDM, where is
v
₂? Make sure to clearly explain how you arrive at your answer.

(c) What starting point
v
₁
should be used so the point
v
₂
computed by the SDM is exactly at the minimum? The point
v
₁
must be located on one of the four sides of the contour plot (in a similar manner as was done in part (a)). Make sure to clearly explain how you arrive at your answer.