I am trying to carry out the Newton's method in Python to solve a problem. I have followed the approach of some examples but I am getting an Overflow Error. Do you have any idea what is causing this?
def f1(x):
return x**3-(2.*x)-5.
def df1(x):
return (3.*x**2)-2.
def Newton(f, df, x, tol):
while True:
x1 = f(x) - (f(x)/df(x))
t = abs(x1-x)
if t < tol:
break
x = x1
return x
init = 2
print Newton(f1,df1,init,0.000001)
Newton's method is
so x1 = f(x) - (f(x)/df(x))
should be
x1 = x - (f(x)/df(x))
There is a bug in your code. It should be
def Newton(f, df, x, tol):
while True:
x1 = x - (f(x)/df(x)) # it was f(x) - (f(x)/df(x))
t = abs(x1-x)
if t < tol:
break
x = x1
return x
The equation you're solving is cubic, so there are two values of x where df(x)=0. Dividing by zero or a value close to zero will cause an overflow, so you need to avoid doing that.
One practical consideration for Newton's algorithm is how to handle values of x near local maxima or minima. Overflow is likely caused by dividing by something near zero. You can show this by adding a print statement before your x= line -- print x and df(x). To avoid this problem, you can calculate df(x) before dividing, and if it's below some threshold, bump the value of x up or down a small amount and try again.
