A paper describes a computational method for solving a problem, and we made a significant improvement to the method and applied it to a new case study. Is it appropriate to publish a response paper?
Most response papers I've seen dispute the findings or methods of the paper they are responding to. Is it reasonable to write a response paper which agrees with the initial paper?
EDIT: It wasn't very clear when I first posted this, but the "response paper" I refer to is a specific mechanism that journals have for responding to an existing paper published in their journal. This is often called a comment or discussion paper. At Nature, they're called "brief communications arising". I might be the only one that calls it a "response paper," actually...
Every paper, in some way, is a response to everything that it cites. You can respond in agreement as much as you can in disagreement. An improvement is a positive response and you might couch it more in terms of a follow-on or follow-up without having to be negative about the prior results.