Multivariate Lagrange interpolation and polynomials of one quaternionic variable

Shayne Waldron


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 $\RR^4$ and $\CC^2$ with good geometric properties, and some aspects of least interpolation and of Kergin interpolation.

Keywords: quaternions, quaternionic polynomials, Lagrange interpolation, Lagrange polynomials, Newton form, Kergin interpolation, least interpolation, quaternionic equiangular lines

Math Review Classification: Primary 12E15, 41A05, 41A10, 41A63, Secondary 12E10, 16D10.

Length: 12 pages

Last Updated: 5 October 2020