The possibility of it being accepted depends on the nature of the improvement. If your improvement, for example, takes it from 100n^3 to30 n^3 operations, your odds of being accepted are very low. If you go from 100n^3 to 100n^2 (or even 10000n^2), and that has never been discovered before, it is definitely publishable. However, even so, it is important that you write in the correct style, because (unfortunately) there are certain conventions, and many journals aren't that friendly to "outsiders". So the advice of getting someone who has published to look at it is very good.

Nevertheless, it depends on the nature of the improvement, as I said above. If you have that, you can be sure that it can eventually be published.