Trial Task

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Task 0

The first consumer calculators provided four arithmetic operators and square root, the latter using an iterative algorithm based on the Newton-Raphson method for finding roots of equations.

To determine the square root of a positive real number k, given any approximation xi > 0 calculate

to obtain a value closer to the root.

Keep applying the formula to obtain better approximations.

Stop when successive approximations differ by 1e–10.

Write a program that calculates the square root of a number read from input.

The initial approximation can be 1 or k, as the algorithm converges quite quickly.

Step 1

Run your program on the following three test cases:

Test Input
2
9.8696044010893586188344909998762
1000000

# My program for the Trial ProgComp competition.

# import SQRT function to compare the calculated result with the computer result

from math import sqrt

testdata = [

9.8696044010893586188344909998762,

1000000

]

#Function to calculate each iteration of the sqrt calculation

def calc(x1):

xi2 = x1 ** 2;

_2xi = 2 * xi

xi1 = xi - (((xi2) - k)/(_2xi))

print(xi1);

return xi1;

# ===========================================================

print ("Newton Raphson Method");

# process each entry in test data list as "k" - the number to find sqrt of

for k in testdata:

xi = float(k);

xi1 = float(0);

while True:

xi1 = calc(xi);

if (abs(xi1 - xi) < 1E-10) :

break; # repeat until the diff is minimal

xi = xi1

print ('Input K = {} -> Calculated SQRT is xi1 = {}, Computer Sqrt = {}'.format(k, xi1, sqrt(k)));

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