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Lecture
Iterative Methods for Linear Equations
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Numerical Analysis: Linear Systems
Covers the analysis of linear systems, focusing on methods such as Jacobi and Richardson for solving linear equations.
Direct Methods for Solving Linear Equations
Explores direct methods for solving linear equations and the impact of errors on solutions and matrix properties.
Numerical Analysis: Stability in ODEs
Covers the stability analysis of ODEs using numerical methods and discusses stability conditions.
Newton's Method for Dynamical Systems
Explores Newton's method for dynamical systems, GMRES, FGMRES, optimization, multishooting, and trust-region methods.
Conjugate Gradient Method
Covers the Conjugate Gradient method for solving linear systems efficiently.
Convergence Analysis: Iterative Methods
Covers the convergence analysis of iterative methods and the conditions for convergence.
Explicit Stabilised Methods: Applications to Bayesian Inverse Problems
Explores explicit stabilised Runge-Kutta methods and their application to Bayesian inverse problems, covering optimization, sampling, and numerical experiments.
Linear Systems Resolution
Summarizes methods for resolving linear systems, including Gaussian elimination and LU decomposition.
Iterative Methods: Linear Systems
Covers iterative methods for solving linear systems and discusses convergence criteria and spectral radius.
Newton's Method: Optimization Techniques
Explores optimization techniques like gradient descent, line search, and Newton's method for efficient problem-solving.
