1. The square root of a real number (p > 0), can be approximated by the...

 

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1. The square root of a real number (p > 0), can be approximated by the limit of the following sequence (Babylonian algorithm). In+1= =(n+1) P In p as n-. Write a script in Python to implement this algorithm (with zo as the initial guess) and compare your the result with the "exact" answer provided by the math.sqrt(p), Here is an outline of the steps to be done. (i) First, perform three iterations of this algorithm for computing the square-root of p=4, starting with the initial guess to 1 (by hand, on paper). = (ii) Construct the algorithm: On a sheet of paper, write the tasks that must be performed (request value from user, read it in, set it equal to xn and calculate the new values In+1 iteratively as a sequence of steps). (iii) How do you decide when to break the iterations? Well, we must choose a pre-specified error tolerance. How do you compute error if the exact root is not known? Use the following stopping criteria in your code. (a) +1 P 1. The square root of a real number (p > 0), can be approximated by the limit of the following sequence (Babylonian algorithm). In+1= =(n+1) P In p as n-. Write a script in Python to implement this algorithm (with zo as the initial guess) and compare your the result with the "exact" answer provided by the math.sqrt(p), Here is an outline of the steps to be done. (i) First, perform three iterations of this algorithm for computing the square-root of p=4, starting with the initial guess to 1 (by hand, on paper). = (ii) Construct the algorithm: On a sheet of paper, write the tasks that must be performed (request value from user, read it in, set it equal to xn and calculate the new values In+1 iteratively as a sequence of steps). (iii) How do you decide when to break the iterations? Well, we must choose a pre-specified error tolerance. How do you compute error if the exact root is not known? Use the following stopping criteria in your code. (a) +1 P