Multivariate Lagrange interpolation and polynomials of one quaternionic variable

This paper considers the extension of classical Lagrange interpolation in one real or complex variable to “polynomials of one quaternionic variable”. To do this, we develop some aspects of the theory of such polynomials. We then give a number of related multivariate polynomial interpolation schemes for R4 and C2 with good geometric properties, and some aspects of least interpolation and of Kergin interpolation.