References
- [1] Ahmad, S.S., Ali, I.: Bounds for eigenvalues of matrix polynomials over quaternion division algebra. Adv. Appl. Cli ord Algebras 26(4), 1095–1125 (2016).10.1007/s00006-016-0640-7
- [2] Barnett, S.: Matrices in control theory with applications to linear programming. Van Nostrand, London (1971).
- [3] Beites, P.D., Nicolás, A.P.: An associative triple system of the second kind. Commun. Algebra 44(11), 5027–5043 (2016).10.1080/00927872.2016.1149185
- [4] Boukas, A, Fellouris, A.: On octonion polynomial equations. Int. J. Math. Comput. Sci. 1(2), 59–73 (2016).
- [5] Cauchy, A.L.: Sur la résolution des équations numériques et sur la théorie de l’élimination. Exercices de Mathématiques. Chez de Bure frères, Paris, 65–128 (1829).
- [6] Chapman, A.: Polynomial equations over octonion algebras. J. Algebra Appl. 19(6), 10 pp. (2020).10.1142/S0219498820501029
- [7] Datt, B., Govil, N.K.: On the location of the zeros of a polynomial. J. Approx. Theory 24, 78–82 (1978).
- [8] Datta, B., Nag, S.: Zero-Sets of quaternionic and octonionic analytic functions with central coefficients. Bull. London Math. Soc. 19(4), 329–336 (1987).
- [9] Dehmer, M.: On the location of zeros of complex polynomials. Journal of Inequalities in Pure and Applied Mathematics 72(26) (2006).
- [10] Dennis, J.E. Jr., Traub, J.F., Weber, R.P.: On the matrix polynomial, lambda-matrix and block eigenvalue problems. Computer Science Department Technical Report, Cornell University, 71–109 (1971).
- [11] Deutsch, E.: Matricial norms. Numer. Math. 16, 73–84 (1970).
- [12] Deutsch, E.: Matricial norms and the zeros of polynomials. Linear Algebra Appl. 3, 483–489 (1970).10.1016/0024-3795(70)90038-8
- [13] Eganova, A., Shirokov, M.I.: Orthomatrices and octonions. Rep. Math. Phys. 20, 1–10 (1984).
- [14] Eilenberg, S., Niven, I., The fundamental theorem of algebra for quaternions, Bull. Amer. Math. Soc. 50, 244–248 (1944).
- [15] Miranda, F., Falcão, M.I.: Modified quaternion Newton methods. In: Murgante B. et al. (eds) Computational Science and Its Applications -ICCSA 2014, June 2014. Lecture Notes in Computer Science, vol 8579, 146–161 Springer, Cham.10.1007/978-3-319-09144-0_11
- [16] Falcão, M.I., Miranda, F., Severino, R., Soares, M.J.: Weierstrass method for quaternionic polynomial root-finding. Mathematical Methods in the Applied Sciences 41(1), 423–437 (2018).10.1002/mma.4623
- [17] Flaut, C., Ştefănescu, M.: Some equations over generalized quaternion and octonion division algebras. Bull. Math. Soc. Sci. Math. Roumanie, 52, 427–439 (2009).
- [18] Higham, N.J., Tisseur, F.: Bounds for eigenvalues of matrix polynomials. Linear Algebra Appl. 358, 5–22 (2003).10.1016/S0024-3795(01)00316-0
- [19] Horn, R., Johnson, C.: Matrix analysis. Cambridge University, New York (2012).
- [20] Jou, Y.-L.: The “Fundamental Theorem of Algebra” for Cayley numbers. Academia Sinica Science Record 3, 29–33 (1950).
- [21] Leite, F.S., Vitória, J.: Generalization of the De Moîvre formulas for quaternions and octonions. Estudos de Matemática, Homenagem a Luís de Albuquerque, University of Coimbra, 121–133 (1991).
- [22] Marden, M.: Geometry of polynomials. American Mathematical Society, Providence, Rhode Island (1966).
- [23] Melman, A.: Generalization and variations of Pellet’s theorem for matrix polynomials. Linear Algebra Appl. 439(5), 1550–1567 (2013).10.1016/j.laa.2013.05.003
- [24] Pellet, A.E.: Sur un mode de séparation des racines des équations et la for-mule de Lagrange. Bulletin des Sciences Mathématiques et Astronomiques 5(1), 393–395 (1881).
- [25] Serôdio, R., Pereira, E., Vitória, J.: Computing the zeros of quaternion polynomials. Comput. Math. with Appl. 42(8–9), 1229–1237 (2001).10.1016/S0898-1221(01)00235-8
- [26] Serôdio, R.: On Octonionic polynomials. Adv. Appl. Cli ord Algebras 17, 245–258 (2007).10.1007/s00006-007-0026-y
- [27] Serôdio, R.: Construction of octonionic polynomials. Adv. Appl. Cli ord Algebras 20, 155–178 (2010).10.1007/s00006-008-0140-5
- [28] Serôdio, R., Ferreira, J.A., Vitória, J.: An iterative method to compute the dominant zero of a quaternionic unilateral polynomial. Adv. Appl. Cli ord Algebras 28, article 45 (2018).10.1007/s00006-018-0866-7
- [29] Serôdio, R., Beites, P.D., Vitória, J.: Eigenvalues of matrices related to the octonions. 4open 2, article 16 (2019).10.1051/fopen/2019014
- [30] Singh, G., Shah, W.M.: On the location of zeros of polynomials. Am. J. Comput. Math. 1(1), 1–10 (2011).10.1007/BF01166551
- [31] Tian, Y.G.: Matrix representations of octonions and their applications. Adv. Appl. Cli ord Algebras 10, 61–90 (2000).10.1007/BF03042010
- [32] Vitória, J.: Matricial norms and lambda-matrices. Revista de Ciências Matemáticas, Universidade Lourenço Marques, 9–28 (1974–75).
- [33] Vitória, J.: Matricial norms and the roots of polynomials. Revista de Ciências Matemáticas, Universidade Lourenço Marques, 51–56 (1974–75).
- [34] Wilf, H.S.: Perron-Frobenius theory and the zeros of polynomials. Proc. Am. Math. Soc. 12(2), 247–250 (1961).
- [35] Ward, J.P.: Quaternions and Cayley numbers. Springer, Dordrecht (1967).