License for library developed with commercial program

Question

I'm developing a commercial application that largely depends on the functionality of a library that will be developed with it. I'd like to open-source this library, because it offers functionality that is not found elsewhere and can be useful in other applications.

However, I will also use it in my own commercial application. I don't want to publish the source of the main application, but it is definitely not a derived work (think of calculator app using GPL licensed library to calculate sine). And if someone else commercially uses the library, I want to require them to publish any changes made.

Is the GPL license suitable for this or is LGPL perhaps what I need?