On Friday, March 31, 2023, at 3pm NDT, Patrick Farrell, from the Numerical Analysis Group at the University of Oxford delivered a public lecture on "The bizarre behaviour of Newton's method for solving equations" in Room 3034B of the Education Building at Memorial University of Newfoundland.

Click here to view recorded lecture.

The bizarre behaviour of Newton's method for solving equations

Newton's method, invented in the 1660's, is the best tool we have for solving mathematical equations. It is used every day to compute weather forecasts, predict satellite trajectories, improve the aerodynamic performance of cars and planes, manage the lithium-ion battery in your phone, and many other things besides. But while it is powerful and fast, its convergence is fickle and bizarre: it may converge to a solution you didn't expect, or get stuck in a loop, or just blow up. While the algorithm itself can be described in one line, its convergence is still poorly understood, even 350 years after its invention.

In this talk I will introduce Newton's method in a friendly and intuitive way, explain what is known about its convergence, demonstrate its bizarre behaviour with live examples, and describe some open challenges to motivate the next generation of mathematicians.