Edexcel A Level Maths: Pure:復習筆記10.1.3 x = g(x) Iteration
x = g(x) Iteration
What does 
?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
- This is a?recurrence relation where, starting with a number
, we will get an answer
?which we can then reuse in the original function - Equations need to be rearranged into an?iterative formula?– ie. the form x = f(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 = f(x)?from your iterative formula
Exam Tip
- 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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