A New Biparametric Family of Two-Point Optimal Fourth-Order Multiple-Root Finders - Young Ik Kim; Young Hee Geum (Journal of Applied Mathematics)
We construct a biparametric family of fourth-order iterative methods to compute multiple roots of nonlinear equations. This method is verified to be optimally convergent. Various nonlinear equations confirm our proposed method with order of convergence of four and show that the computed asymptotic error constant agrees with the theoretical one.