Richardson Iteration Step

Problem

Perform one Richardson iteration step for the system A*x = b:

x_new = x + omega * (b - A*x)

The scalar omega controls the step size and convergence.

Hint

The update is a step of size omega along the residual direction.

case 1

in: [[[4,1],[1,3]],[1,2],[0,0],0.25]

expected: [0.25,0.5]

case 2

in: [[[1,0],[0,1]],[2,4],[1,1],0.5]

expected: [1.5,2.5]

case 3

in: [[[2,0],[0,2]],[0,0],[1,2],1]

expected: [-1,-2]

case 4

in: [[[1,0],[0,1]],[1,1],[3,4],0]

expected: [3,4]

Starter codePython

def richardson_step(A, b, x, omega):
    # Your code here
    pass

4 test cases · run your code against them in the editor