Complete orthonormal sets of polynomial solutions of the Riesz and Moisil-Teodorescu systems in \(\mathbb R^{3}\)
type: Item
instance of: scholarly article
title: Complete orthonormal sets of polynomial solutions of the Riesz and Moisil-Teodorescu systems in \(\mathbb R^{3}\)
zbMATH Open document ID: 1206.30067
author: Isabel Cação
published in: Numerical Algorithms
publication date: 2010-10-13T00:00:00Z
review text: The author constructs complete orthonormal sets of polynomial solutions of the well-known Riesz system. Starting from Fueter polynomials in the description of H. R. Malonek, the procedure of orthonormalization by Gram-Schmidt is numerical unstable and great time-consuming. As an alternative, a family of Appell homogeneous monogenic polynomials (solutions of the Riesz-system) is deduced. This system has much better numerical properties. A similar construction also works for the Moisil-Teodorescu system. Recently, such questions are in the focus of several authors and therefore intensively studied.
Mathematics Subject Classification ID: 30G35
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 42C05
zbMATH DE Number: 5799430
zbMATH Keywords: spherical harmonics
zbMATH Keywords: Riesz system
zbMATH Keywords: Moisil-Teodorescu system
zbMATH Keywords: homogeneous monogenic polynomials
zbMATH Keywords: orthogonal polynomials
MaRDI profile type: Publication
full work available at URL: s11075-010-9411-z
OpenAlex ID: W2057205723
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DOI: 10.1007/S11075-010-9411-Z
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description: scientific article; zbMATH DE number 5799430