My advice to you is to find a different PS that supplies 9-12V output. An LM317 regulator will accept up to 40V on its input, but it will convert the voltage difference between it's input and output to heat. Therefore, to keep the heating to a minimum, you'll want to keep the difference between the input voltage and the LM317 output to a minimum. Depending on space, a computer power supply can be ideal as it supplies 12V, 5V, and 3.3V DC output.