Modifications of Newton’s method for even‐grade palindromic polynomials and other twined polynomials

The paper describes some modifications of Newton’s method for refining the zeros of even‐grade f(x)‐twined (f(x)‐egt) polynomials, defined as polynomials whose roots appear in pairs {x i ,f(x i )}. Particular attention is given to even‐grade palindromic (egp) polynomials. The algorithms are derived from certain symmetric division processes for computing a symmetric quotient and a symmetric remainder of two given f(x)‐egt 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.