Objectives Exposure to using double variables, while loops, and static methods E

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Objectives

Exposure to using double variables, while loops, and static methods

Exposure to using several Eclipse features including creating a project by copying an existing project, renaming a Java file using refactoring, deleting files, creating a file by copying an existing file, using the Java editor, and exporting a project

The Problem

Your first job is to create a Java program that repeatedly asks the user whether they wish to calculate another square root. If the response is "y", then the program should proceed; if it is anything else, then the program should quit. Whenever it proceeds, the program should prompt the user for a number (a positive double, and your program may simply assume the input is consistent with this requirement) and then report the square root of that number to within a relative error of no more than 0.01%. The computation must be done using Newton iteration.

The intuitive idea of Newton iteration for computing square roots is fairly straightforward. Suppose you have a guess r for x1/2 that is too large; the argument is similar if it is too small. If r is too large to be the square root of x, then x/r must be too small, so the average of r and x/r should be a better guess than either r or x/r. This suggests that if you repeatedly replace your current guess r by (r + x/r)/2, then your sequence of guesses should converge to x1/2. And indeed it can be proved that it does. A good initial guess for x1/2 is simply r = x. If you continue updating r until |r2

Explanation / Answer

//Newton2.java

//Newton3.java

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