A new method for roots of monic quaternionic quadratic polynomial

DOI10.1016/j.camwa.2009.08.034zbMath1189.65090OpenAlexW2012076756MaRDI QIDQ979852

Xue-Han Cheng, Mei-Xiang Zhao, Zhi-Gang Jia

Publication date: 28 June 2010

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2009.08.034

zbMATH Keywords

quaternionmonic quaternionic quadratic polynomialreal quadratic formreal quadratic form matrices

Mathematics Subject Classification ID

Finite-dimensional division rings (16K20) Numerical computation of roots of polynomial equations (65H04)

Related Items (11)

On the zeroes of Clifford algebra-valued polynomials with paravector coefficients ⋮ Newton method in the context of quaternion analysis ⋮ On solutions of second-order matrix polynomial equation of high degree ⋮ Solution of a quadratic quaternion equation with mixed coefficients ⋮ Algorithms for quaternion polynomial root-finding ⋮ Scalar-vector algorithm for the roots of quadratic quaternion polynomials, and the characterization of quintic rational rotation-minimizing frame curves ⋮ Complex Roots of Quaternion Polynomials ⋮ Some new quaternionic quadratics with zeros in terms of second order quaternion recurrences ⋮ Zeros of two-sided quadratic quaternion polynomials ⋮ Cubic formulas for computing the zeros of certain quaternionic polynomial ⋮ Roots of quaternion polynomials: theory and computation

Cites Work

• Unnamed Item
• Computing quaternionic roots by Newton's method
• The fundamental theorem of algebra for Hamilton and Cayley numbers
• On the zeros of polynomials over arbitrary finite dimensional algebras
• A new theory of regular functions of a quaternionic variable
• Zeros of unilateral quaternionic polynomials
• On the Structure of the Set of Zeros of Quaternionic Polynomials
• ON THE ZEROS OF POLYNOMIALS OVER QUATERNIONS
• On the Zeros of Polynomials over Division Rings
• Equations in Quaternions
• The Roots of a Quaternion
• The “fundamental theorem of algebra” for quaternions
• Computing the zeros of quaternion polynomials.

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