Question: Use the direct gradient descent algorithm (9.120) using the value of d k found in Exercise 9.6.14 to solve the linear systems in Exercise 9.6.7.

Use the direct gradient descent algorithm (9.120) using the value of d_kfound in Exercise 9.6.14 to solve the linear systems in Exercise 9.6.7. Compare the speed of convergence with that of the Conjugate Gradient Method.

Data From Exercise 9.6.14

In (9.120), find the value of d_k that minimizes p(x_k+1).

Data From Exercise 9.6.7

Solve the following linear systems by the Conjugate Gradient Method, keeping track of the residual vectors and solution approximations as you iterate.

Xk+1=X+d r where Ik = b - Axk. (9.120)

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