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Don't forget that the regulator will disipate more heat that the wattage of the fan because it is absorbing more than half the power from your supply. Put it on a heat sink.
As Gary says. The regulator does not actually need the capacitors to work but HF noise on the lines can be reduced by proper by-passing on the input and output. Those high capacity electrolytic capacitors are not particularly effective against HF noise. A .01ufd ceramic will be better for this.
Barry
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