Course introduction
1. Course Overview
2. Course Activities
3. Getting Python
Day 1.
Direct Solvers and Matrix Decompositions
Matrix form of equations
Gaussian Elimination
Matrix decompositions
LU decomposition
Cholesky decomposition
QR decomposition
Day 2.
Sparse Matrices and Iterative Solvers
Sparse matrices
COOrdinate format
Finite Difference Matrix
Scipy.sparse and problems
Iterative methods
Jacobi and Relaxation Methods
Krylov subspace methods and CG
Iterative solvers in Scipy
Day 3.
Solving ODEs
ODE Solvers - AM exercise
ODE Solvers - PM exercise
Day 4.
Non-linear Optimisation
Nonlinear Optimisation
Line Search Methods
Trust Region Methods
Derivative-free methods
Finite difference method
Nelder-Mead method
Day 5.
Applied Bayesian Inference
Applied Bayesian Inference - AM exercise
Applied Bayesian Inference - PM exercise
Day 6-8.
Projects
Project description
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Sparse Matrices and Iterative Solvers