Tom's definition doesn't put any specific value on the number of equations. Combo believes that a PID is an algorithm. I can write that as a single equation. That doesn't make it any less an algorithm.
L D[AR2,P#0.0]'s definition is good too. It focuses on procedure more than characters. I think most of us assume that an algorithm is a bit stronger than just concept. We expect to get something we can just plug numbers into and get a result. However, I don't thnk that expectation is a requirement, semantically speaking.
As far as authorship, keep in mind that automation has been around long enough that authoring something completely original is pretty rare. If you just mention in casual conversation that you developed an algorithm for solving some problem I don't think many people will have an issue with claiming authorship, assuming you actually authored it, even if it is a repeat of something someone else did. Re-inventing the wheel is not a crime. However, if you are going to use this algorithm as a personal selling point I would be more careful. Once a procedure is published I believe it is free to use. However, if someone catches you in what they perceive as a lie, even though you may not knowingly be lying, your credibility could take a hit. For example, you develop a PID gain scheduling algorithm that you think is unique. You claim original authorship of it. Gain scheduling is pretty common. If someone finds a paper from 1955 that details your scheme they will believe you just copied it and claimed authorship, even though you just happened to independently develop the same scheme.
The one exception to his is if you are using an algorithm that is an exclusive part of a patented system. That would be a problem. That would typically happen if you were an employee of one company, left that company and used the algorithm either on your own or with a different company. The court might look at that a little funny. But as a twist, if you independently develop an algorithm that is the same as a proprietary part of a patented process and you had no reasonable way of knowing what that algorithm was before you developed it, I think people would be OK with you claiming ownership.
Keep in mind I'm not a patent attorney. this is just based on what I have picked up over the years. Tom, Peter, Mike and others who do this kind of thing for a living probably have a better feel than I do.
Keith