Confluent Vandermonde matrices, divided differences, and Lagrange–Hermite interpolation over quaternions

ABSTRACT

We introduce the notion of a confluent Vandermonde matrix with quaternion entries and discuss its connection with Lagrange–Hermite interpolation over quaternions. The formula for the rank of a confluent Vandermonde matrix is obtained as well as the representation formula for divided differences of quaternion polynomials. Extensions of these results to the power series setting include the formula for the rank of a confluent Cauchy matrix and norm-constrained Lagrange–Hermite interpolation by square summable power series over quaternions.

KEYWORDS:

• Confluent Vandermonde matrix
• Lagrange–Hermite interpolation

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 12E15
• 15B33
• 65D05