Modifications of Newton's method for even-grade palindromic polynomials and other twined polynomials
The authors present some modifications of the Newton method for the iterative refinement of the roots of a palindromic polynomial of even degree. These modifications rely upon certain structured division processes for palindromic polynomials generating a quotient and a remainder with the same property of the coefficients. Analogous results also hold for other kinds of \(f(x)\)-twined polynomials. Numerical results indicate that the presented algorithms can be more accurate than other methods which do not take into consideration the symmetry of the coefficients.
scientific article; zbMATH DE number 6117963