Lecture 20: Overview, review and looking forward

Lecture 20: Overview, review and looking forward#

Floating point numbers
- Representations and rounding
- \(eps\), machine precision
Matrices and vectors
- Multiplication
- Inner product
- Euclidean norms
Systems of linear equations
- Translating between matrices and systems of linear equations
- Deriving simple linear systems of equations
- Solving triangular systems of equations
- Gaussian Elimination
- LU factorisation
- Jacobi iteration
- Gauss Seidel iteration
- Initial guesses, convergence and stopping criteria
Dynamic problems
- Derivatives, gradients/slopes and rates of change
- Reading and drawing simple graphs
- Deriving models for simple dynamic problems
- Initial conditions
- Euler’s method
- Midpoint scheme
Nonlinear equations
- Roots of an equation
- Bisection algorithm
- Newton’s method
- Quasi Newton methods
- Hybrid methods
Data fitting
- How to form a system of linear equations to find a simple curve of best fit
- How to find a best fit solution
- When to choose which curve (from a simple choice)
- Problems with our approach

You will apply ideas from this course in many areas of computer science including
- graphics;
- artificial intelligence/machine learning.
There are plenty of opportunities for Final Year Projects on topics in numerical computation. If you are interested talk to me (or your tutorial leader).
There are also funded places for further study in numerical computation….

Thank you for your attention!

Good luck with your exam and future studies

I hope you have a good Christmas break!