I’m making an attempt to plot a Niave Algorithm to seek out the roots to Quaternion Polynomials.
I believed I had discovered an answer within the article Newton Technique within the Context of Quaternion Evaluation, as a Newton Technique that works over the Quaternions is strictly what I would like. The problem is that, if I understood the strategy accurately, it’s essential to know the worth of the quaternion earlier than you possibly can derive it… a minimum of thats what it seems to be like on this comparable article: Algorithms for quaternion polynomial root-finding. The problem with that’s the function of this venture is to approximate the quaternion roots, which is pointless if I do know their actual worth.
Is there an iterative algorithm that can do that? i.e. Discover a minimum of one root given a Quaternion Polynomial?
Be aware: I would love a algorithm that could possibly be carried out on Mathematica, so it must be repeatedly reproduceable.