Answer to Question #237724 in Linear Algebra for lavanya

Question

Employ the Gauss-Seidel method, solve the system.

10𝑥 + 𝑦 + 𝑧 = 12

2𝑥 + 2𝑦 + 10𝑧 = 14

2𝑥 + 10𝑦 + 𝑧 = 13

Answer 1

# 10x + y + z = 12      -> x = (12-y-z)/10
# 2x + 10y + z = 13     -> z = (13-2x-z)/10
# 2x + 2y + 10z = 14    -> y = (14-2x-2y)/10

f1 = lambda x,y,z: (12-y-z)/10
f2 = lambda x,y,z: (13-2*x-z)/10
f3 = lambda x,y,z: (14-2*x-2*y)/10

x0 = 0
y0 = 0
z0 = 0
n = 1

# tolerable error
err = 0.001

print("Gauss Seidel Iteration")
print('\nIterations\tx\t\ty\t\tz\n')

Flag = True
while(Flag):
    x1 = f1(x0,y0,z0)
    y1 = f2(x1,y0,z0)
    z1 = f3(x1,y1,z0)
    print('%d\t%8.4f\t%8.4f\t%8.4f\n' %(n, x1,y1,z1))
    err1 = abs(x0-x1);
    err2 = abs(y0-y1);
    err3 = abs(z0-z1);
    
    n =n+1
    x0 = x1
    y0 = y1
    z0 = z1
    
    Flag = (err1>err and err2>err and err3>err)

print('\nOutput Solution: x=%0.3f, y=%0.3f and z = %0.3f\n'% (x1,y1,z1))