EXPANSION OF INTERPOLATION IN THE OCTONIONS CONTEXT

Abstract

This paper extends the notion of interpolation from the quaternionic framework to the octonionic setting. By establishing a well-adapted algebraic basis, we examine how replacing the quaternion space with octonions influences the generated curves. The obtained curves in the octonionic space are not only differentiable but also display smoother behavior compared to those generated by corresponding methods in the quaternionic case. Moreover, the convergence is achieved with less iteration.