High-Order Iterative Methods Repeating Roots a Constructive Recapitulation

This paper considers practical, high-order methods for the iterative location of roots nonlinear equations, one at a time. Special attention is being paid to algorithms also applicable multiple initially known and unknown multiplicity. Efficient are presented in this note evaluation multiplicity index root sought. Also reviewed here super-linear super-cubic that converge contrarily or alternatingly, enabling us, not only approach briskly confidently but actually bound bracket it as we progress.