Scientific Computing

Learning Outcomes

Subject Specific Practical Skills

Having successfully completed this module you will be able to:

• Gain facility in benchmarking and optimising numerical algorithms
• Gain facility in using numerical computing libraries
• Be able to model simple problems such that they can be solved numerically

Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

• Demonstrate knowledge of a range of tools and techniques for solving numerical problems
• Understand and reason about the numerical implications of the properties of linear algebra
• Understand how real numbers are stored on digital computers and the implications with respect to precision, accuracy and errors

Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

• Choose and justify the choice of appropriate algorithms for particular tasks
• Assess numeric stability and convergence of numeric algorithms

Error Analysis

Floating-point arithmetic and IEEE 754

Absolute and relative error in Taylor’s approximation

Numerical Methods for Nonlinear Equations

Bisection

Fixed Point Iteration

Newton’s Method

Numerical Linear Algebra

Least Squares Methods: e.g., Gauss-Seidel, Newton, Levenberg–Marquardt algorithm

Condition number, Stability and Sensitivity

Power methods and Eigen-decomposition

Singular Value Decomposition and Pseudo inverse

LU, Cholesky, QR, Gram-Schmidt process

(Optional) Krylov subspace

Numerical Methods for Calculus and Differential Equations

Numerical Integration

Introduction to Ordinary Differential Equations

Euler’s Method and Runge-Kutta Method

Brief introduction to PDE and Finite Difference Method

Solving Large-scale problems

Numerical Library, e.g., BLAS, LAPACK and Sparse BLAS

Parallelism, Block-wise computation and GPU acceleration

(Optional) Randomised Methods

The module consists of:

• Lectures
• Combined tutorials and computing laboratory sessions

Summative

This is how we’ll formally assess what you have learned in this module.

Referral

This is how we’ll assess you if you don’t meet the criteria to pass this module.

Repeat

An internal repeat is where you take all of your modules again, including any you passed. An external repeat is where you only re-take the modules you failed.