Solution of a quadratic quaternion equation with mixed coefficients. (May 2016)

• Record Type: Journal Article
• Authors: Farouki, Rida T.; Gentili, Graziano; Giannelli, Carlotta; Sestini, Alessandra; Stoppato, Caterina
• Is Part Of: Journal of symbolic computation. Volume 74(2016)
• Page Start: 140
• Page End: 151
• Publication Date: 2016-05
• Subjects: Quadratic quaternion equations -- Polynomials with mixed quaternion coefficients -- Circular roots -- 3-Sphere roots -- Surface construction -- Pythagorean-hodograph curves; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2015.06.007
• Languages: English
• ISSNs: 0747-7171

Abstract

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 .