An improved iterative technique for polynomial factorisation employing a quasi-newton approach

An iterative procedure based on the Newton-Raphson process for the factorisation (splitting) of a real-coefficient polynomial into two lower-degree polynomials is described in summary, and the method extended to the case where the Jacobian matrix is not updated at each iteration (a `Quasi-Newton´ process). It is demonstrated that a faster process results, and that in the case of a particular class of problems, an optimal rate of update of the Jacobian matrix can be determined. the modified convergence criteria are examined but without proof at this stage