Mathematics Grade 11 Investigation Task

Mathematics                                           Grade 11                                           Investigation Task

Due date: 16 April 2009

 

N.B. This task will form part of your portfolio assessed using the attaché Rubric.

Successive Approximation Algorithm

Successive approximation is an iterative algorithm for approximating the square root of a number. The algorithm is based on the following observations:

If x is the square root of N then,
(1)    (N/x) = x so
(2)    (x + (N/x)) / 2 = x.

It can be shown that if y is an approximation of the square root of N then,
(3)    (y + (N/y)) / 2 is a better approximation.

Using equation (3) repeatedly allows an approximation for the square root of N to be continuously refined. The refinement of the approximation may be stopped once the difference between successive approximations is less than some threshold.