Extension of Bairstow's Method for Multiple Quadratic Factors

On Bairstow’s method for the solution of polynomial equations

“…Thus, in particular, if (z2 + p*z + q*) is a quadratic factor of multiplicity greater than one, then /* = 0. For this case Arthur [2] and Carrano [5] have independently suggested a modification which retains the property of quadratic convergence from a sufficiently close starting point, at some computational expense.…”