References
- Niven I . Equations in quaternions. Amer Math Monthly. 1941;48:654–661.
- Serôdio R , Pereira E , Vitória J . Computing the zeros of quaternion polynomials. Comput Math Appl. 2001;42(8):1229–1237.
- De Leo S , Ducati G , Leonardi V . Zeros of unilateral quaternionic polynomials. Electron J Linear Algebra. 2006;15:297–313.
- Falcão MI . Newton method in the context of quaternion analysis. Appl Math Comput. 2014;236:458–470.
- Miranda F , Falcão MI . Modified quaternion Newton’s method. In: Murgante B , et al., editors. Lecture notes in computer science. Cham: Springer; Vol. 8579(part 1); 2014. p. 146–161.
- Pogorui AA , Shapiro M . On the structure of the set of zeros of quaternionic polynomials. Complex Var Theory Appl. 2004;49(6):379–389.
- Serôdio R , Siu L-S . Zeros of quaternion polynomials. Appl Math Lett. 2001;14(2):237–239.
- Janovská D , Opfer G . A note on the computation of all zeros of simple quaternionic polynomials. SIAM J Numer Anal. 2010;48(1):244–256.
- Erdo\v{g}du M , Özdemir M . Two-sided linear split quaternionic equations with \textit{n} unknowns. Linear Multilinear Algebra. 2015;63(1):97–106.
- Janovská D , Opfer G . Linear equations and the Kronecker product in coquaternions. Mitt Math Ges Hamburg. 2013;33:181–196.
- Janovská D , Opfer G . Zeros and singular points for one-sided coquaternionic polynomials with an extension to other ℝ4 algebras. Electron Trans Numer Anal. 2014;41:133–158.
- Özdemir M . The roots of a split quaternion. Appl Math Lett. 2009;22(2):258–263.
- Pogoruy AA , Rodríguez-Dagnino R . Some algebraic and analytical properties of coquaternion algebra. Adv Appl Clifford Algebra. 2010;20(1):79–84.
- Janovská D , Opfer G . The number of zeros of unilateral polynomials over coquaternions and related algebras. Electron Trans Numer Anal. 2017;46:55–70.
- Antonuccio F . Split-quaternions and the Dirac equation. Adv Appl Clifford Algebr. 2015;25(1):13–29.
- Erdo\v{g}du M , Özdemir M . On eigenvalues of split quaternion matrices. Adv Appl Clifford Algebr. 2013;23(3):615–623.
- Brenner JL . Matrices of quaternions. Pacific J Math. 1951;1(3):329–335.
- Falcão MI , Miranda F , Severino R , et al . Polynomials over quaternions and coquaternions: a unified approach. In: Gervasi O , et al., editors. Lecture notes in computer science. Cham: Springer; Vol. 10405; 2017. p. 379–393.
- Kula L , Yayli Y . Split quaternions and rotations in semi euclidean space E4 2 . J Korean Math Soc. 2007;44:1313–1327.
- Lam TY . A first course in noncommutative rings. New York: Springer; 1991.
- Gordon B , Motzkin TS . On the zeros of polynomials over division rings. Trans Amer Math Soc. 1965;116:218–226.
- Smoktunowicz A , Wróbel I . On improving the accuracy of Horner’s and Goertzel’s algorithms. Numer Algorithms. 2005;38(4):243–258.
- Falcão MI , Miranda F , Severino R , et al . Evaluation schemes in the ring of quaternionic polynomials. Bit Numer Math. 2018 Mar;58(1):51–72 . DOI:10.1007/s10543-017-0667-8
- Eilenberg S , Niven I . The ‘fundamental theorem of algebra’ for quaternions. Bull Amer Math Soc. 1944 Apr;50(4):246–248.