I'm sorry, but to be honest, I doubt they would be terribly interested, as there are too many problems that would arise. I assume you hope they would pay you for your algorithm, maybe license it, or whatever, but even that would involve some significant issues. Paying you for the algorithm, would mean they would need to keep it secret, hidden underneath a compiled wall, but it also sounds like you have not published any details of the code. (Because it sounds as if you want to keep it secret, lest someone might steal your idea.) That means any users of that code would then be left completely in the dark as to how the code works. And external users of code often want to be able to provide references. For example, someone writing their doctoral thesis often needs to fully document what was done. As I recall, thesis committees tend not to be happy at seeing the words ... "and then a miracle occurs".
Even beyond that, many users of MATLAB require the code to be certified as valid. Thse who work for certain institutions, for example, might require a certification. And if a user cannot verify the code as being valid, this is a bad thing for any significant computation. And if your idea is as great as you think it is, it would be "significant".
Of course, you should realize that splines are already pretty easy to compute, and you would need to show that your scheme is truly an innovation. Why should someone pay you for an idea that, while technically interesting, offers no real benefit over an already easy computation?
All of this means that in order for your work to be used, it probably needs externally, peer reviewed publication on your part. So you should just publish your idea. Show that it is an innovation. Do so in a peer reviewed journal. And then, if it really is useful, you might find others start to use it. At least then you would get some recognition for your idea.
Another idea might be for you to gain employment at TMW. Once you are inside the door, you could propose your idea as an enhancement to those specific codes. Of course, even then, I'd bet they would need you to have already published the idea, as again, they usually try wherever possible to provide references indicating the source of the algorithms in their code. Hey, the good news is, TMW is a fun place to work, and there are very many wonderful people working there. (That said by someone who is not an employee of TMW, and never has been. But I know many people there, and to the extent that my word is worth anything, I have huge respect for them all.)
