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    Newtom's method using Java

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    The NewtonsSquareRoot Class
    ? Writing a class using conditionals that test double values
    ? Writing a class using a while loop
    The project directory should include the following:
    ? NewtonsSquareRoot.java
    ? NewtonsSquareRootTest.java
    To approximate the square root of a positive number n using Newton's method, you need to make an initial guess at the root and then refine this guess until it is "close enough." Your first initial approximation should be root = 1; A sequence of approximations is generated by computing the average of root and n/root.
    Use the constant:
    private static final double EPSILON = .00001;
    Your loop for findSquareRoot should behave like this:
    make the initial guess for root
    while ( EPSILON < absolute value of the difference between root squared and n )
    calculate a new root
    return root
    Your class should have a constructor that takes the number you want to find the square root of. Implement the usual accessor method(s) and a findSquareRoot method that uses Newton's method described above to find and return the square root of the number. Add a method setNumber that takes a new number that replaces the number in the instance field. Supply a toString method that returns a string containing the number and the square root of the number.
    Your test class should:
    ? Instantiate a NewtonsSquareRoot object using the number 1.
    ? Print the square root of 1 using the toString method.
    ? Use a while loop to generate the numbers 2 through 100.
    ? In the loop use the setNumber and toString methods to find and print the square roots of all the numbers from 2 to 100 inclusive.

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    Solution Preview

    This solution shows how to use Newton's Method to estimate the square root of a number. The class NewtonsSquareRoot encapsulates this functionality.

    Newton's method for finding a square root ...

    Solution Summary

    This solution implements Newton's method to estimate a square root.