Question

using python with only using import math and copy no other powerful functions.

Write a function defined as: def GaussSeidel(Aaug, x, Niter = 15):

Purpose: use the Gauss-Seidel method to estimate the solution to a set of N linear equations expressed in matrix form as Ax = b. Both A and b are contained in the function argument – Aaug.

Aaug: an augmented matrix containing [A | b ] having N rows and N+1 columns, where N is the number of equations in the set.

x: a vector (array) contain the values of the initial guess Niter: the number of iterations (new x vectors) to compute

return value: the final new x vector.

Write and call a main() function that uses your GaussSeidel function to estimate and print the solution to the sets of linear equations contained in the following Augmented A-matrices:

MyA = [[4, -1, -1, 3], [-2, -3, 1, 9], [-1, 1, 7, -6]] using initial guesses of all zeros. Perform 22 iterations.

anotherA = [[4, 3, 1, -1, 2], [2, -5, 0, -2, -3], [-3, 3, -6, 1, 5], [0, 1, 4, 8, -2]] using initial guesses of all zeros. Perform 3 iterations.

Answer 1

GauSied.py 1 def GaussSeidel (Aaug, x, Niter = 15): N = len(x) for n in range (Niter): for i in range (N): res = Aaug[i][N] It = list(range (N)) It.remove(i) for j in It: res -= Aaug[i][j]*x[j] res/= Aaug[i][i] x[i] = res return x 13 def main(): myA = [[4, -1, -1, 3], [-2, -3, 1, 9], [-1, 1, 7, -6]] sol = GaussSeidel (myA, [0, 0, 0], 22) print("Solution of myA: ", *sol) anotherA = [[4, 3, 1, -1, 2], [2, -5, 0, -2, -3], [-3, 3, -6, 1, 5], [0, 1, 4, 8, -2]] sol = GaussSeidel (anotherA, [0, 0, 0, 0], 3), print("Solution of anotherA:", *sol) 22 if _name_=='_main__': main() 24