# Multivariate Lagrange interpolation and polynomials of
one quaternionic variable

## Shayne Waldron

## Abstract:

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

## Availability: