On Numerical Aspects of Pseudo-Complex Powers in ℝ3

  • Carla Cruz
  • M. Irene Falcão
  • Helmuth R. Malonek
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8579)


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.


Pseudo-complex powers monogenic polynomails Vandermonde matrix 


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Carla Cruz
    • 1
  • M. Irene Falcão
    • 2
  • Helmuth R. Malonek
    • 1
    • 3
  1. 1.Centro de Investigação e Desenvolvimento em Matemática e AplicaçõesUniversidade de AveiroPortugal
  2. 2.Departamento de Matemática e Aplicações and Centro de MatemáticaUniversidade do MinhoPortugal
  3. 3.Departamento de MatemáticaUniversidade de AveiroPortugal

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