Finding Fixed Points: Iterative Methods for Convergence

This lecture introduces the concept of fixed points of a function, explaining how to iteratively find them using initial estimates and repetitive applications of the function until convergence. The instructor presents a programmatic solution for finding fixed points, focusing on the example of calculating square roots. Various attempts and refinements are discussed, including the use of average damping to control oscillations. The lecture also explores functions as return values, showcasing the power of passing and returning functions in programming. Finally, a square root function formulation using fixedPoint and averageDamp is provided, emphasizing the importance of abstraction and reuse in programming.