Lab03.md

Newton Raphson Method

Algorithm

1. Start

2. Define function as f(x)

3. Define first derivative of f(x) as g(x)

4. Input initial guess (x0), tolerable error (e) 

5. Initialize iteration counter i = 1

6. If g(x0) = 0 then print "Mathematical Error" and goto (11) otherwise goto (7) 

7. Calcualte x1 = x0 - f(x0) / g(x0)

8. Increment iteration counter i = i + 1

9. If |f(x1)| > e then set x0 = x1 and goto (6) otherwise goto (11)

10. Print root as x1

11. Stop

Source Code

# Defining Function
def f(x):
    return x**3 - 5*x - 9

# Defining derivative of function
def g(x):
    return 3*x**2 - 5

# Implementing Newton Raphson Method
def newtonRaphson(x0,e):
    print('\n\n*** NEWTON RAPHSON METHOD IMPLEMENTATION ***')
    step = 1
    flag = 1
    condition = True
    print('Iteration\t\tx1\t\tf(x1)\t\tError')
    while condition:
        if g(x0) == 0.0:
            print('Divide by zero error!')
            break
        
        x1 = x0 - f(x0)/g(x0)
        err = (x1 - x0)/x1
        print('%d\t\t%0.6f\t%0.6f\t\t%0.6f'%(step, x1, f(x1), err))
        
        x0 = x1
        step = step + 1
        
        condition = abs(f(x1)) > e
    
    if flag==1:
        print('\nRequired root is: %0.8f' % x1)
    else:
        print('\nNot Convergent.')

#Note: You can combine above three section like this
x0 = float(input('Enter Guess: '))
e = float(input('Tolerable Error: '))

# Starting Newton Raphson Method
newtonRaphson(x0,e)

Output

Link

Newton Raphson Method

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