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Title: On numerical aspects of pseudo-complex powers in R^3
Other Titles: On numerical aspects of pseudo-complex powers in ℝ3
Author: Cruz, Carla
Falcão, Maria Irene
Malonek, Helmuth Robert
Keywords: Pseudo-complex powers
Monogenic polynomials
Vandermonde matrix
Issue Date: 2014
Publisher: Springer International Publishing
Abstract: In this paper we consider a particularly important case of 3D monogenic polynomials that are isomorphic to the integer powers of one complex variable (called pseudo-complex powers or pseudo-complex polynomials, PCP). The construction of bases for spaces of monogenic polynomials in the framework of Clifford Analysis has been discussed by several authors and from different points of view. Here our main concern are numerical aspects of the implementation of PCP as bases of monogenic polynomials of homogeneous degree k. The representation of the well known Fueter polynomial basis by a particular PCP-basis is subject to a detailed analysis for showing the numerical efficiency of the use of PCP. In this context a modification of the Eisinberg-Fedele algorithm for inverting a Vandermonde matrix is presented.
Peer review: yes
DOI: 10.1007/978-3-319-09144-0_1
ISBN: 978-3-319-09143-3
ISSN: 0302-9743
Appears in Collections:CIDMA - Comunicações

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