Function Iteration |
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Let us consider the following scenario. You are playing a serious soccer game and it begins to rain and the playing field has turned into a huge muck. (Our experience has been that soccer games never stop, unless a natural disaster occurs.) As a result, the white soccer outfits got really dirty, and your mother thinks it needs to be washed at least twice. Now there are two ways of getting second washing. One way is after the first washing, buy another washing machine for the second washing. This is illustrated in figure 3 by two washing machines which are arranged in series, so that you can put output of the first washing machine which is still dirty, back into the second washing machine as its input. But, rather than buying another washing machine, a more practical |
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Figure 3. Two washing
machines connected in series |
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way is indicated in figure 4. That is, we run the same washing machine twice by recycling the output of first washing as input for the second washing. This therefore introduces a couple of strange terms. We first say running a function over and over is iteration, and the result or output of iteration is called the iterate. By chance, if the output of second washing, i.e., the second iterate, is not clean enough, you may go through the third washing or iteration, and so on, until you are happy with the final iterate. |
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Figure 4. Washing
iteration |
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