Is there anywhere I can find some kind of database on all known stars and their properties (mass, surface temperature, radius, and luminosity)? I have been looking for some kind of collection of all known stars and their individual respective mass/radius/temperature/and luminosity, can you link me to one if it exists?

My goal is to write an algorithm that creates polynomial functions that calculate a stars temp/lum/radius based on mass. I know there are existing equations, however the ones I have found are more troublesome and imprecise compared to if I could use polynomial functions I create myself.

The Hertzsprung-Russel diagram ( http://upload.wikimedia.org/wikipedia/commons/1/17/Hertzsprung-Russel_StarData.png ) is a great example of representation of what data I need, however it's axes are not constant, so I can not visually gather accurate sample data to deduce any functions.

Edit: Essentially even a large quantity of estimates will suffice. I intend to use this data to generate a semi-realistic galaxy for an MMO I am developing, so it doesn't by any means need to be perfect.
There really isn't anything as comprehensive as you want. And, we don't have accurate information for all of these variables for a large number of stars.

The two main problems are masses and radii.

Really the only set of stars that have both measured masses and radii are those in eclipsing binary systems. If these binary stars also have distances, measured by parallax, then the components could also have luminosity estimates and estimates of effective temperature.
The best catalogue I can recommend is that compiled by John Southworth, containing perhaps a 100 systems.

http://www.astro.keele.ac.uk/jkt/debcat/

If you just want a mass, but can cope without a radius, then you can also include components of astrometric binary systems. There is a well-known paper by Delfosse et al. (2000) containing stellar masses and luminosities.