Task 04
Task 04ΒΆ
deadline: 21/03/2021 23:59 CET
[0.25 points]: Edit the conjugate gradient method so that it returns a list of all iterations \( x^{(k)} \) (including the initial guess).
[0.25 points]: Solve the following system of linear equations
\[
4 x_1 + x_2 = 1,
\]
\[
x_1 + 3x_2 = 2
\]
using the edited conjugate gradient method withe the error tolerance of \( 10^{-15} \). Print the list of all iterations \( x^{(k)} \).
[0.5 points]: Plot the iterations \( x^{(k)} \) and the contours of the function
\[
f(x) = 1 \, / \, 2 \, x^T \mathbb{A} x - x^T b, \ x \in [-1, 1] \times [-1, 1],
\]
where \( \mathbb{A} \) is the coefficient matrix and \( b \) is the right-hand side vector, using the matplotlib.pyplot.scatter and the matplotlib.pyplot.contour functions, respectively.
# add your code here