Alycia is currently a second-year student studying a Bachelor of Mathematical Science at the University of South Australia. She is interested in applied mathematics, specifically linear programming and calculus. Another interest of hers is numerical analysis which she intends to explore in her project.
Study of a Generalised Newton Method for Solution of Nonlinear Equations
The celebrated Newton method and its extensions have been a powerful and essential tool in solving nonlinear equations arising in many disciplines. As a result, new properties of the Newton method are studied and novel extensions constantly developed and tested. Recently, a generalisation of the single-variable Newton method has been proposed by means of a function that can be chosen freely. The generalised Newton method is quadratically convergent like the original Newton method.
The aim of this project is to (i) carry out extensive numerical experiments with a wide library of nonlinear equations, (ii) do further mathematical analysis of some of the existing results and (iii) investigate an extension of the generalised method to at least some special cases of multi-variable nonlinear equations.