Applied Numerical Methods with MATLAB, 3rd edition, Steven C. Chapra

chapra 3.13 & chapra 4.1

3.13 The divide and average method, an old-time method for approximating the square root of any positive number a, can be formulated as x = x + a/x 2 Write a well-structured M-file function based on the while...break loop structure to implement this algorithm. Use proper indentation so that the structure is clear. At each step estimate the error in your approximation as ? = xnew ? xold xnew Repeat the loop until ? is less than or equal to a specified value. Design your program so that it returns both the result and the error. Make sure that it can evaluate the square root of numbers that are equal to and less than zero. For the latter case, display the result as an imaginary number. For example, the square root of ?4 would return 2i. Test your program by evaluating a = 0, 2, 10 and ?4 for ? = 1 10?4.

4.1 The divide and average method, an old-time method for approximating the square root of any positive number a, can be formulated as x = x + a/x 2 Write a well-structured function to implement this algorithm based on the algorithm outlined in Fig. 4.2.

Do not use the "while-break" structure

Do not use the square root function, sqrt

The sample code includes a table output. Use it to help you debug your code. You do not need to generate a table output.

Take care of the main part of the problem first, then deal with the special cases

Don't forget to include input validation, for example, the input must be scalar