Lagrange interpolation problem for quaternion polynomials
type: Item
instance of: scholarly article
title: Lagrange interpolation problem for quaternion polynomials
zbMATH Open document ID: 1303.30042
author: Vladimir Bolotnikov
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2014-09-04T00:00:00Z
review text: The classical Lagrange interpolation problem over the field of complex numbers has some relevance in several branches of mathematics. For instance, it is important in approximation theory, numerical analysis and control theory. A generalization over other finite fields will open up further applications. The author considers the Lagrange problem over the skew-field of real quaternions. Left and right problems arise. Algebraical means that solvability criterions are formulated and a solution is derived. It should be mentioned that there exists a paper by \textit{K. Gürlebeck} [Wiss. Inf. 34, 21 S. (1982; Zbl 0551.41004)] which provides a complete construction of a monogenic (i.e., included in the kernel of the Dirac operator) quaternionic (left) Lagrange interpolation polynomial, on the basis of total analytic variables. This result can also be found in the book by \textit{K. Gürlebeck} and the reviewer [Quaternionic analysis and elliptic boundary value problems. Basel: Birkhäuser (1990; Zbl 0850.35001)].
Mathematics Subject Classification ID: 30G35
Mathematics Subject Classification ID: 41A05
zbMATH DE Number: 6339665
zbMATH Keywords: Lagrange interpolation problem
zbMATH Keywords: quaternions
MaRDI profile type: Publication
full work available at URL: j.crma.2014.05.008
OpenAlex ID: W2072033611
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DOI: 10.1016/J.CRMA.2014.05.008
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description: scientific article; zbMATH DE number 6339665