Numerical Linear Algebra (MA30051/MA50178) Winter Term 2018/2019

This is the website for the course MA30051: Numerical Linear Algebra, which can be taken as part of a BSc or an MMath degree.It can also be taken as part of an MSc Course or SAMBa, in which case the course is called MA50178.

Prerequisites for the course are Analysis and Algebra as well as standard courses on Numerical Analysis.

## What previous participants have said about this course:

- 'Very good explanations.'
- 'Lecturer is approachable and engaging.'
- 'Really enjoyed the module. Thanks.'
- 'This is a really great unit, couldn't recommend enough.'
- 'I really enjoyed this module and the coursework set, thank you!'

## Timetable

- Lectures: Monday 15:15 in CB 3.1 and Tuesday 9:15 in CB 3.5
- Problem Classes: Thursday 16.15 in CB 5.1
- Office Hour: Friday 11:15 in 4W 5.11 (If you cannot make this I am available after the lecture or you can just book an appointment at a different time by email.)

## Some helpful links

- Unit decription for MA30051 (from catalogue)
- Unit decription for MA50178 (from catalogue)
- MATLAB Primer (A MATLAB manual)
- Mathworks pages a very useful source for any Matlab issues

## Some Literature (all available in the library)

- G. H. Golub, C. F. Van Loan:
*Matrix Computations*(3rd ed.) Johns Hopkins University Press Baltimore, MD, USA, 1996. - B. N. Parlett:
*The Symmetric Eigenvalue Problem*, SIAM, Philadelphia, 1998. - J. W. Demmel:
*Applied Numerical Linear Algebra*, SIAM, Philadelphia, 1997. - L. N. Trefethen, D. Bau, III:
*Numerical Linear Algebra*, SIAM, Philadelphia, 1997.

## Lecture notes

- Cover Sheet
- Table of Contents
- Chapter 1
- Chapter 2
- Chapter 3 Information on GMRES and MINRES, more general methods for solving linear systems with any square nonsingular (nonsymmetric) A. Information on Preconditioning.
- Chapter 4
- Chapter 5

## Handouts

- Introduction
- Handout 1 on PageRank.
- Handout 2 on Inner products and norms.
- Handout 3 on the Jordan Canonical Form.
- Handout 4 on the Jacobi method.
- Handout 5 on the Gauss-Seidel method.
- Handout 6 on the Steepest Descent method.
- Handout 7 on the Conjugate Gradient method.
- Handout 8 on the Power method.
- Handout 9 on the Inverse Iteration.
- Handout 10 on the QR method.
- Handout 11 on the Householder reflection and the Hessenberg/tridiagonal reduction.

## Matlab codes

- Chapter 2: Jacobi.m, Jacobialpha.m, GaussSeidel.m
- Chapter 3: steepestdescent.m, conjgrad.m
- Chapter 4: powermethod.m ipower.m, rqi.m
- Chapter 5: qrfact.m, QRmethod.m,vhouse.m, houshess.m

## Problem Sheets

If you would like individual feedback on your solutions to the problem sheets, please hand them in during the lecture on Tuesday (or in the p/hole on level 1 by Wednesday 4:15pm at the latest) for the problem class on Thursday.

- Problem Sheet 1 Solutions to Problem Sheet 1
- Problem Sheet 2 Solutions to Problem Sheet 2, Example code for Question 4
- Problem Sheet 3, Hints Solutions to Problem Sheet 3, Jacobi Code for Question 5, Gauss-Seidel Code for Question 5 Some info on the Gershgorin Circle Theorem
- Problem Sheet 4, Hints Solutions to Problem Sheet 4, Code for Question 8, Code for Question 9
- Problem Sheet 5, Hints Solutions to Problem Sheet 5, Code for Question 6ab , Code for Question 6c uses mycg.m and mysteepestdescent.m
- Problem Sheet 6, Hints Solutions to Problem Sheet 6, Code for Question 6
- Problem Sheet 7, Hints Solutions to Problem Sheet 7, Code for Question 4, Code for Question 5
- Problem Sheet 8 Solutions to Problem Sheet 8, Code for Question 5(i), Code for Question 5(ii)

## Assignment

- Assignment set on Thursday 15th November and due Monday 3rd December 2018 (at 1.00 pm in 4W, level 1) - the Matlab code should be submitted via Moodle.
- The Matlab files for Question 6 are here.
- Coursework Cover Sheet.

## Class Test

Students taking the MA50178 version course will have to do a class test in addition to the assignment and the exam. This 60 minute written class test will take place on

**11th January 2019 at 10:15 in 8W 2.13**.

Below is the reading material for the class test and an exam from the previous year.

- Least squares
- CGLS (You don't need to know Section 8.2).
- Class test 2016

I would like you to know how to solve a least squares problem using the normal equtions, the QR decomposition, and the SVD, and how you would do it iteratively using CGLS. The above material is sufficient but you can use any books and papers you like to study the methods.

## Exam

#### The exam takes place in January 2019.

- Here is an Exam Revision Guide

## Other interesting stuff

- An enthusiastic TED-talk about the beauty of matrices: TED-talk by Margot Gerritsen (Stanford).
- An article about the QR algorithm and John Francis and a news item

If you have any queries, please come and see me either after the lecture or in my office (4W 5.11) or send me an email.