Gauss - Siedal Method

AIM: Write a Python program to solve the system of linear equations using Gauss - Siedal method.

Source Code:

# Gauss Seidel Iteration

# Defining equations to be solved in diagonally dominant form
f1 = lambda x,y,z: (17-y+2*z)/20
f2 = lambda x,y,z: (-18-3*x+z)/20
f3 = lambda x,y,z: (25-2*x+3*y)/20

# Initial setup
x0 = 0
y0 = 0
z0 = 0
count = 1

# Reading tolerable error
e = float(input("Enter tolerable error: "))

# Implementation of Gauss Seidel Iteration
print("Count\tx\ty\tz")

condition = True

while condition:
  x1 = f1(x0,y0,z0)
  y1 = f2(x1,y0,z0)
  z1 = f3(x1,y1,z0)
  print("%d\t%0.4f\t%0.4f\t%0.4f" %(count, x1,y1,z1))
  e1 = abs(x0-x1)
  e2 = abs(y0-y1)
  e3 = abs(z0-z1)
 
  count += 1
  x0 = x1
  y0 = y1
  z0 = z1
 
  condition = e1>e and e2>e and e3>e

print("Solution: x=%0.3f, y=%0.3f and z = %0.3f"% (x1,y1,z1))

Output:

Enter tolerable error: 0.01

Count	x	y	z
1	0.8500	-1.0275	1.0109
2	1.0025	-0.9998	0.9998
3	1.0000	-1.0000	1.0000

Solution: x=1.000, y=-1.000 and z = 1.000