This expository paper traces the development of the Newton-Raphson method for solving nonlinear algebraic equations through the extant notes, letters, and publications of Isaac Newton, Joseph Raphson, ...

The term after the minus sign is the Newton-Raphson step. If the likelihood function evaluated at is less than that evaluated at ,then is recomputed using half the step size. The iterative scheme ...

Modified Newton-Raphson solution for dispersion equation of transition water waves is proposed for practical applications. The wave dispersion equation is a nonlinear equation.