Example: Setting Up Test Harnesses

• To compute the square root of a use a common algorithm:
  1. Guess a value x that might be somewhat close to the desired square root (x = a is ok)
  2. Actual square root lies between x and a/x
  3. Take midpoint (x + a/x) / 2 as a better guess
     
  4. Repeat the procedure. Stop when two successive approximations are very close to each other
• Method converges rapidly. Square root of 100:

  Guess #1: 50.5
  Guess #2: 26.24009900990099
  Guess #3: 15.025530119986813
  Guess #4: 10.840434673026925
  Guess #5: 10.032578510960604
  Guess #6: 10.000052895642693
  Guess #7: 10.000000000139897
  Guess #8: 10.0