This module presents concepts and methods of numerical analysis. It introduces the learner to the idea of finding approximate solutions to mathematical problems by constructing procedures and algorithms and analysing their efficiency.
1. Introduction: Computer representation of numbers; Computational errors, loss of significance, stability and convergence of algorithms.
2. Root finding techniques for nonlinear equations. The bisection method; Newton's method; The secant method; Fixed-point iteration algorithms and convergence conditions; Error analysis and comparison between different methods.
3. Systems of linear equations. Linear algebra review; Gaussian elimination with different pivoting strategies; The LU and Cholesky factorization; Iterative methods (Jacobi and Gauss-Seidel algorithms) and their convergence properties;
4. Random number generating algorithms. Modular arithmetic, the middle square method and the linear congruential method.
5. Sorting Algorithms. Selection sort, bubble sort, merge sort and quick sort.
Lectures supported by problem-solving tutorials and laboratory sessions using mathematical software packages.
| Module Content & Assessment | |
|---|---|
| Assessment Breakdown | % |
| Formal Examination | 70 |
| Other Assessment(s) | 30 |