Practice
Euler's Method
Design and code a main program that prompts for
and accepts a floating-point number and an error
margin and calculates the approximate square root
of the number using Euclid's method. Do not
use the sqrt function from
the math library.
Euclid's method keeps guessing the square root of
a number, say x, using the
formula
where estimate is the
most recent estimate of the square root of x.
The method improves each estimate by taking the average of
the estimate and the
quotient as defined
above. The improvement process terminates
once the difference between the
estimate and the quotient is within a
prescribed error margin, say epsilon:
| quotient - estimate | <= epsilon
|
Euclid's method starts with an initial estimate of
If the number input by the user is
positive or zero, your program displays successive estimates
in tabular form, something like:
Find the Square Root of : 34567.0
Acceptable Error : 0.000000001
Iteration Estimate
1 17283.500000000000
2 8642.750000000000
3 4323.374768592173
4 2165.685071502284
5 1090.823151320520
6 561.256032187495
7 311.422339911770
8 211.209757516741
9 187.435851925555
10 185.928139870331
11 185.922026767594
12 185.922026667095
The approximate square root after 12 iterations is 185.922027
|
If the number input is negative, your program does not
calculate a square root and simply displays a
message to that effect.
|
