SOME EFFICIENT MODIFIED HOUSEHOLDER ITERATIVE SCHEMES FOR NONLINEAR EQUATIONS (FUDMA JOURNAL OF SCIENCES, 2024)
The Householder scheme is a well-known iterative scheme for estimating the solution of nonlinear equation. Its major setbacks includes low convergence order, non-optimal and require high function derivative evaluation assessment in an iteration cycle. In this manuscript, we offered an iterative scheme that is an extension of the Householder scheme. In order to circumvent the highlighted setbacks of the Householder scheme, its modified form that is of convergence order four, optimal and require no second function derivative is put forward. The scheme was further modified via the use of weight functions to scale its convergence order from four to eight at the expense of one additional function evaluation and still retains its optimality property. The performance measures on the developed schemes was carried out by comparing their computational performance with that of some existing robust schemes.
Keywords: Iterative schemes; Nonlinear equations; Householder scheme; Optimal order of convergence