units

FIT3085

Faculty of Information Technology

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# Monash University Handbook 2010 Undergraduate - Unit

### 6 points, SCA Band 2, 0.125 EFTSL

 Level Undergraduate Faculty Faculty of Information Technology Offered Not offered in 2010 Coordinator(s) Associate Professor David Dowe

#### 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 have -
A knowledge and understanding of:

• the way in which computer arithmetic approximates the conventional arithmetic used in Mathematics;
• how errors caused by inexact computer arithmetic can propagate throughout the execution of a numerical algorithm;
• how errors may be reduced by an iterative numerical process and understand different kinds of convergent behaviour;
• how the local approximation paradigm may be used to construct iterative algorithms for solving numerical problems;
• how Gaussian Elimination may be used to solve simultaneous systems of linear equations;
• how the paradigm of matrix transformation can be used to construct algorithms for solving problems in numerical linear algebra;
• how vector and matrix norms are used to determine the stability of matrix transformations for solving problems in numerical linear algebra;
• how knowledge of eigenvalues and eigenvectors can be used to determine the stability of matrix transformations for solving problems in numerical linear algebra;
• basic algorithms for solving simultaneous systems of linear equations, such as Gaussian elimination, partial and full pivotting, LU factorisation and matrix inversion;
• orthogonal matrices and their use in constructing unconditionally stable numerical algorithms.
• least squares solution of overdetermined systems of linear equations;
• some aspects of robust statistics such as leverage points and outliers.
Developed attitudes that enable them to:
• appreciate the level of difficulty involved in producing reliable and efficient numerical algorithms for particular kinds of numerical problems;
• question the accuracy and reliability of any result produced by numerical software.
Developed the skills to:
• write software that uses iterative algorithms and tests for convergence;
• program fundamental numerical linear algorithms;
• establish systematically that a program for solving numerical linear algebra problems has been implemented correctly.
Demonstrated the communication and teamwork skills necessary to:
• communicate how a numerical algorithm is performing with respect to stability and rate of convergence or divergence;
• explain the extent to which an answer produced by a numerical program can be trusted.

#### Assessment

Examination (3 hours): 70%; In-semester assessment: 30%

#### Contact hours

2 hrs lectures/wk

#### Prerequisites

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