I can guess that your potentiometer is used for instrumentation, like a displacement transducer. Many transducers, like LVDTs exhibit an output/input graph shaped like an "S", which can be easily "linearized" with a polynomial equation to improve the precision of the sensor. On a potentiometer, the "input vs output" curve may not look at all like an "S". A look-up table may be the only way to go, with individual calibration, as Chuckles159 mentioned. Be careful with repeatability, it may ruin your efforts to improve the precision of the pot.