TASK: Write a script that estimates the square root of 2017 using averaging.
COMMENT: One way to approximate the square root of a number x starts with any positive guess "r" and then repeatedly replaces r by a new estimate:
r = ( r + x/r) / 2
INSTRUCTIONS:
Use MATLAB's sqrt() function to set the variable "s" to the exact value
of the square root of 2017.
s = ?;
Use the name "r" for the variable that stores your estimate.
Give r an initial value of 1, and have r printed out.
r = 1
Your estimation error "e" is | r - s |.
Compute "e" using MATLAB's abs() function, and have e printed out.
e = abs ( ? )
Replace r by the average of r and 2017/r, and have it printed out.
Recompute e, because r has changed, and have it printed out.
r = ?
Carry out the "replace and recompute" steps 6 times.
(Use "cut and paste" in your editor to repeat the steps.)
If your script is correct, then except for the very first step,
you should see the size of the error e decreasing each time.
After 6 steps, the error should be less than 10.
SUBMIT: Your work should be stored in a script file called "hw001.m". Your script file should begin with at least three comment lines:
% hw001.m
% YOUR NAME
% This script (describe what it does)
% Add any comments here that you care to make.
If this problem is part of an assignment, then submit it to Canvas.