Gauss-Seidel Iteration One Step

Problem

Perform one Gauss-Seidel iteration step for A*x = b from the guess x0, updating in place:

x_new[i] = (b[i] - sum over j != i of A[i][j] * x[j]) / A[i][i]

Already updated components are used immediately. Assume nonzero diagonal.

Hint

Unlike Jacobi, the first updated entry is immediately used by later rows.

case 1

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

expected: [0.25,0.5833333333333334]

case 2

in: [[[2,0],[0,4]],[4,8],[0,0]]

expected: [2,2]

case 3

in: [[[3,-1],[-1,2]],[5,3],[0,0]]

expected: [1.6666666666666667,2.3333333333333335]

case 4

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

expected: [0,0.6666666666666666]

Starter codePython

def gauss_seidel_step(A, b, x0):
    # Your code here
    pass

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