A comprehensive analysis of the morphology of the solution space for a special type of quadratic quaternion equation is presented. This equation, which arises in a surface construction problem, incorporates linear terms in a quaternion variable and its conjugate with right and left quaternion coefficients, while the quadratic term has a quaternion coefficient placed between the variable and its conjugate. It is proved that, for generic coefficients, the equation has two, one, or no solutions, but in certain special instances the solution set may comprise a circle or a 3–sphere in the quaternion space H. The analysis yields solutions for each case, and intuitive interpretations of them in terms of the four–dimensional geometry of the quaternion space H.

Solution of a quadratic quaternion equation with mixed coefficients / Farouki, Rida; Gentili, Graziano; Giannelli, Carlotta; Sestini, Alessandra; Stoppato, Caterina. - In: JOURNAL OF SYMBOLIC COMPUTATION. - ISSN 0747-7171. - STAMPA. - 74:(2016), pp. 140-151. [10.1016/j.jsc.2015.06.007]

Solution of a quadratic quaternion equation with mixed coefficients

GENTILI, GRAZIANO;GIANNELLI, CARLOTTA;SESTINI, ALESSANDRA;STOPPATO, CATERINA
2016

Abstract

A comprehensive analysis of the morphology of the solution space for a special type of quadratic quaternion equation is presented. This equation, which arises in a surface construction problem, incorporates linear terms in a quaternion variable and its conjugate with right and left quaternion coefficients, while the quadratic term has a quaternion coefficient placed between the variable and its conjugate. It is proved that, for generic coefficients, the equation has two, one, or no solutions, but in certain special instances the solution set may comprise a circle or a 3–sphere in the quaternion space H. The analysis yields solutions for each case, and intuitive interpretations of them in terms of the four–dimensional geometry of the quaternion space H.
2016
74
140
151
Farouki, Rida; Gentili, Graziano; Giannelli, Carlotta; Sestini, Alessandra; Stoppato, Caterina
File in questo prodotto:
File Dimensione Formato  
Solution-of-a-quadratic-quaternion-equation-with-mixed-coefficients_2016_Journal-of-Symbolic-Computation.pdf

Accesso chiuso

Tipologia: Pdf editoriale (Version of record)
Licenza: Tutti i diritti riservati
Dimensione 332.77 kB
Formato Adobe PDF
332.77 kB Adobe PDF   Richiedi una copia
AAM-JSC-2016.pdf

accesso aperto

Tipologia: Versione finale referata (Postprint, Accepted manuscript)
Licenza: Tutti i diritti riservati
Dimensione 232.41 kB
Formato Adobe PDF
232.41 kB Adobe PDF

I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1002590
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 6
  • ???jsp.display-item.citation.isi??? 4
social impact