Introduces iterative methods for linear equations, convergence criteria, gradient of quadratic forms, and classical force fields in complex atomistic systems.
Explores explicit stabilised Runge-Kutta methods and their application to Bayesian inverse problems, covering optimization, sampling, and numerical experiments.
Explores gradient descent methods for smooth convex and non-convex problems, covering iterative strategies, convergence rates, and challenges in optimization.
Covers the concept of gradient descent in scalar cases, focusing on finding the minimum of a function by iteratively moving in the direction of the negative gradient.
Introduces Newton's method for solving non-linear equations iteratively, highlighting its fast convergence but also its potential failure to converge in some cases.
Explores the concept of stationary distribution in Markov chains, discussing its properties and implications, as well as the conditions for positive-recurrence.