Confluent Vandermonde matrices, divided differences, and\n Lagrange-Hermite interpolation over quaternions

2015/05/13 by Vladimir Bolotnikov, Bolotnikov, Vladimir
Engineering · Computer Science · Mathematics · #Advanced Numerical Analysis Techniques #Matrix Theory and Algorithms #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.1505.03574

Abstract

We introduce the notion of a confluent Vandermonde matrix with quaternion\nentries and discuss its connection with Lagrange-Hermite interpolation over\nquaternions. Further results include the formula for the rank of a confluent\nVandermonde matrix, the representation formula for divided differences of\nquaternion polynomials and their extensions to the formal power series setting.\n

Citations

• Theory of Non-Commutative Polynomials

Related

• Confluent Vandermonde matrix and related topics
• History of confluent Vandermonde matrices and inverting them algorithms
• New approaches for solving linear confluent Vandermonde systems and inverse of their corresponding matrices via Taylor's expansion
• Confluent Vandermonde with Arnoldi
• Multivariate Lagrange interpolation and polynomials of one quaternionic variable