x = g(x) Iteration (Edexcel A Level Maths): Revision Note
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x = g(x) Iteration
What does xn + 1 = g(xn) mean?
When an equation cannot be solved using the usual analytical methods, we can still find approximate solutions to a certain degree of accuracy
Iteration is one way to do this, by repeatedly using each answer as the new starting value for a function, we can achieve an ever more accurate answer
Iterations are shown using the notation xn + 1 = g(xn)
This is a recurrence relation where, starting with a number (xn), we will get an answer xn + 1 which we can then reuse in the original function
Equations need to be rearranged into an iterative formula – ie. the form x = g(x)
Iteration diagrams
Iterations can be shown on diagrams called staircase or cobweb diagrams
These can be drawn by plotting the graphs of y = x against y = g(x) from your iterative formula
Examiner Tips and Tricks
You must show all your steps when rearranging an equation into an iterative formula
Working backwards can often be helpful to figure out how an equation has been rearranged but you must write your answer as if you worked forwards
Use ANS button on your calculator to calculate repeated iterations
Keep track of your iterations using x2, x3… notation
Iteration may be part of bigger numerical methods questions
Worked Example
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