ALGEBRAIC METHODS - ITERATIVE FORMULA

(Section 28 of Higher Maths – student support book by Banks and Alcorn,

2007)

Process of iteration has three stages: 1. Rearrange equation to form an iterative formula 2. Chose a starting value, x1 3. Substitute the starting value, and then values of xn, into the iterative

formula. Continue the process until the required degree of accuracy is obtained.

(Basically all it means is keep substituting the x value until you find the answer) Find a solution to the equation: X^ - 4x -3 = 0

Answer: X = 4.6

x X^ - 4x – 3 = 0

3 3^ - (4 x 3) -3 = -6 4 4^ - (4 x 4) -3 = -3

4.6 4.6^ - (4x4.6) -3 = -0.24 4.64 4.64^ – (4 x 4.64) – 3 = 0.07 (1 decimal space)

The Xn needs to be close to the answer. X3 + x = 40 Answer: x = 3.3

x X3 + x = 40

3 33 + 3 = 30 (so the value of ‘x’ must be higher than 3)

4 34 + 4 = 85 ( value of ‘x’ must be lower than 4) 3.3 3.33 + 3.3 = 39.2 (continue finding the value between 3 and

4 until you get the answer as close to the 40)