Write a computer program in Python for \"EXAMPLE 5.5\" on page 136 EXAMPLE 5.5 F

Question

Write a computer program in Python for "EXAMPLE 5.5" on page 136

EXAMPLE 5.5 False Position Problem Statement. Use the false-position method to determine the root of the same equation investigated in Example 5.1 [Eq (E5.1.)]. Solution. As in Example 5.3, initiate the computation with guesses of x,-12 and 16 First iteration: xi = 12 x" = 16 x,= 16- f(x) = 6.1139 f(x")=-2.2303 2.2303(12- 16) 6.1139 (2.2303) = 14.309 which has a true relative error of 0.88 percent. Second iteration: f(x)f(x) -1.5376

Explanation / Answer

'''
A bisection method in python starting with interval [a,b] with tolrrance accuracy acc
f(x) = x^2 - 7
'''

def f(x):
   return math.pow(x,2) - 7

def biection_method(a,b,tol):
    if f(a)*f(b) > 0:
       print("No root found")
    else:
       while (b-a)/2.0 > acc:
           nextx = b - (f(b)*(a-b))/f(a)-f(b)
           if f(nextx) == 0:
               return nextx
           elif f(a)*f(nextx) < 0:
                b = nextx
           else:
                a = nextx
      return(nextx)

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