Modified Householder Iterative Scheme requiring no Function Derivative for Solving Nonlinear Equations.

The Householder iterative scheme (HIS) for determining solution of equations that are nonlinear have existed for over fifty decades and have enjoyed several modifications in literature. However, in most HIS modifications, they usually require function derivative evaluation in their implementation. Obtaining derivative of some functions is difficult and in some cases, it is not achievable.To circumvent this setback, the divided difference operator was utilised to approximate function derivatives that appear in the scheme. This resulted to the development of a new variant of the HIS with high precision and require no function derivative. The theoretical convergence of the new scheme was established using Taylor’s expansion approach. From the computational results obtained when the new scheme was tested on some non-linear problems in literature, it performed better than the Householder scheme.