Question

Newton's method in Python

The polynomial function

Implement the polynomial function. The function computes where .

def poly(x, a, b, c, d):
    #
    # complete
    #
    pass

The derivative of the polynomial

Implement the derivative function given by .

def poly_der(x, a, b, c, d):
    #
    # complete
    #
    pass

Newton's method

Implement Newton's method by updating the solution guess iteratively. The function returns a tuple of .

def newtons_method(a, b, c, d, n, x0):
    #
    # complete
    #
    pass

poly(10, 1, 2, 3, 4)

poly_der(10, 1, 2, 3, 4)

newtons_method(1, 2, 3, 4, n=10, x0=0.0)

Answer 1

#while pasting the tabs/indentations may get disturbed, please refer pic for correct tabs
def poly(x, a, b, c, d):
return a*x**3 +b*x**2+c*x+d;

def poly_der(x,a,b,c,d):
return 3*a*x**2 +2*b*x+c;

def newtons_method(a,b,c,d,n,x0):
count=0;
x=x0;
while(count<=n):
x=x0-(poly(x0, a, b, c, d)/poly_der(x0,a,b,c,d))
x0=x
count=count+1;
return (x,poly(x, a, b, c, d))

print(newtons_method(1,2,3,4,10,0))