Monash University

Leader(s): David Dowe

Offered

Not offered in 2009

Synopsis

This unit is intended to teach students about the design of numerical algorithms and the effect that computer arithmetic has on both the design of numerical algorithms and on numerical software. Students are introduced to main paradigms for creating numerical computing algorithms, namely the paradigm of local approximation and the paradigm of matrix transformations.

Objectives

At the completion of this unit, students will be able to understand:

1. the way in which computer arithmetic approximates the conventional arithmetic used in Mathematics;
2. how errors caused by inexact computer arithmetic can propagate throughout the execution of a numerical algorithm;
3. how errors may be reduced by an iterative numerical process and understand different kinds of convergent behaviour;
4. how the local approximation paradigm may be used to construct iterative algorithms for solving numerical problems;
5. how Gaussian Elimination may be used to solve simultaneous systems of linear equations;
6. how the paradigm of matrix transformation can be used to construct algorithms for solving problems in numerical linear algebra.
7. how vector and matrix norms are used to determine the stability of matrix transformations for solving problems in numerical linear algebra;
8. how knowledge of eigenvalues and eigenvectors can be used to determine the stability of matrix transformations for solving problems in numerical linear algebra;
9. basic algorithms for solving simultaneous systems of linear equations, such as Gaussian elimination, partial and full pivotting, LU factorization and matrix inversion.
10. orthogonal matrices and their use in constructing unconditionally stable numerical algorithms;
11. least squares solution of overdetermined systems of linear equations;
12. some aspects of robust statistics such as leverage points and outliers.

At the completion of this unit, students will have attitudes that allow them to:

1. appreciate the level of difficulty involved in producing reliable and efficient numerical algorithms for particular kinds of numerical problems.;
2. question the accuracy and reliability of any result produced by numerical software.

At the completion of this unit, students will be able to:

1. write software that uses iterative algorithms and tests for convergence;
2. program fundamental numerical linear algorithms;
3. establish systematically that a program for solving numerical linear algebra problems has been implemented correctly;
4. communicate how a numerical algorithm is performing with respect to stability and rate of convergence or divergence;
5. explain the extent to which an answer produced by a numerical program can be trusted.

Assessment

Examination 70%, 2 Practical Assignments 30%

Contact hours

2 x contact hrs/week

Prerequisites

FIT2004 or CSE2304 and FIT2014 or CSE2303 and 12 points of mathematics

Prohibitions

CSE2307

Additional information on this unit is available from the faculty at:

http://www.infotech.monash.edu.au/units/fit3085