Polynomials and Vandermonde matrices over the field of quaternions.
Zero points of quadratic matrix polynomials
Our aim is to classify and compute zeros of the quadratic two sided matrix polynomials, i.e. quadratic polynomials whose matrix coefficients are located at both sides of the powers of the matrix variable. We suppose that there are no multiple terms of the same degree in the polynomial , i.e., the terms have the form , where all quantities are square matrices of the same size. Both for classification and computation, the essential tool is the description of the polynomial by a matrix equation...
Computing quaternionic roots by Newton's method.
Fast Givens transformation for quaternion valued matrices applied to Hessenberg reductions.
On Convergence and Quasiregularity of Interpolating Complex Planar Splines.
A survey of some recent results on Clifford algebras in
We will study applications of numerical methods in Clifford algebras in , in particular in the skew field of quaternions, in the algebra of coquaternions and in the other nondivision algebras in . In order to gain insight into the multidimensional case, we first consider linear equations in quaternions and coquaternions. Then we will search for zeros of one-sided (simple) quaternion polynomials. Three different classes of zeros can be distinguished. In general, the quaternionic coefficients can...
The Derivation of Cubic Splines with Obstacles by Methods of Optimization and Optimal Control.
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