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General


Semester

Autumn 2009 (Monday, October 5 to Friday, December 11)

Timetable

  • Tue 12:05 - 12:55
  • Thu 11:05 - 11:55

Prerequisites

Undergraduate analysis and linear algebra.

Syllabus

This is a 20 lecture course. The aim of the course is to introduce students to a number of key ideas and methods in numerical analysis and for the students to learn to implement algorithms in Matlab.
Syllabus  
Lecture 1:   Introduction and prerequisites. Description of the ideas to be covered and the assessment activities.
Lecture 2:   Stable and unstable computation, relative and absolute error, floating point computation and round off errors.
Lecture 3:   Finding roots of nonlinear equations. Bisection, secant and Newton's methods.
Lecture 4:   Approximation of functions I. Polynomial interpolation, Lagrange and Newton forms: divided differences.
Lecture 5:   Approximation of function II. Piecewise polynomial approximation. Splines and their generalisations into higher dimensions.
Lecture 6:   Approximation of functions III. Least squares and orthogonal polynomials.
Lecture 7:   Numerical integration. Newton-Cotes and Gauss formulae. Integration of periodic functions. Romburg integration.
Lecture 8:   The Fast Fourier transform.
Lecture 9:   Wavelets I.
Lecture 10:   Wavelets II.
Lecture 11:   Solving systems of linear equations I. Gauss elimination, pivoting. Cholesky factorisation.
Lecture 12:   Solving systems of linear equations II. Conditioning and error analysis.
Lecture 13:   Solving systems of linear equations II. Iterative methods: Jacobi, Gauss-Seidel, SOR.
Lecture 14:   Least squares solution, Schur decomposition, the QR and QZ algorithms.
Lecture 15:   Power method and singluar value decomposition.
Lecture 16:   Krylov subspace methods: Arnoldi algorithm.
Lecture 17:   Conjugate gradient method and GMres.
Lecture 18:   Functions of a matrix.
Lecture 19:   This lecture will be set aside for expansion of topics in the course previously.
Lecture 20:   Summarising and finishing course. This lecture also allows some time if other topics take longer than expected.


Reading list and references  

There are a number of excellent books on numerical analysis and you are encouraged to consult these books for alternative and often better accounts of what you have heard in lectures. In the main I have followed Kincaid and Cheney [4] and Higham [2].
  1. S. D. Conte and C. deBoor, Elementary Numerical Analysis, (3rd Ed) McGraw-Hill, 1980.
  2. N. J Higham, Accuracy and Stability of Numerical Algorithms, SIAM, 1996.
  3. A. Iserles, A First Course in the Numerical Analysis of Differential Equations, CUP, 1996.
  4. D. R. Kincaid and E. W. Cheney, Numerical Analysis, Brooks/Cole Publishing Company, 1991.
  5. E. Süli and D. Myers, An Introduction to Numerical Analysis, CUP, 2003.

Lecturer


Jeremy Levesley
Email jl1@mcs.le.ac.uk
Phone (0116) 2523897
Interests Approximation theory, numerical analysis
Photo of Jeremy Levesley


Students


Photo of Hanefa Al-Qasmi
Hanefa Al-Qasmi
(Manchester)
Photo of Mohd Alazah
Mohd Alazah
(Reading)
Photo of Sabrina Blackwell
Sabrina Blackwell
(Loughborough)
Photo of Ashley Brereton
Ashley Brereton
(Liverpool)
Photo of FAIRHURST David
FAIRHURST David
(Leicester)
Photo of Aiman Elragig
Aiman Elragig
(Exeter)
Photo of Saadia Farid
Saadia Farid
(Manchester)
Photo of Donatello Gallucci
Donatello Gallucci
(Newcastle)
Photo of PAUL GUNS
PAUL GUNS
(Cardiff)
Photo of Raja Zafar Iqbal
Raja Zafar Iqbal
(Birmingham)
Photo of Muhammad Anjum Javed
Muhammad Anjum Javed
(Newcastle)
Photo of Kieron Rhys Moore
Kieron Rhys Moore
(Loughborough)
Photo of Stephen Rickaby
Stephen Rickaby
(East Anglia)
Photo of Badr Saad Al-Kahtani
Badr Saad Al-Kahtani
(Manchester)
Photo of Mousa Shaikh-Soltan
Mousa Shaikh-Soltan
(Manchester)
Photo of Chris Welshman
Chris Welshman
(Manchester)


Bibliography


Elementary Numerical AnalysisConte
Accuracy and stability of numerical algorithmsHigham
A first course in the numerical analysis of differential equationsIserles
Numerical analysisKincaid
An introduction to numerical analysisSüli and Mayers


Note:

Clicking on the link for a book will take you to the relevant Google Book Search page. You may be able to preview the book there. On the right hand side you will see links to places where you can buy the book. There is also link marked 'Find this book in a library'. This sometimes works well, but not always. (You will need to enter your location, but it will be saved after you do that for the first time.)

Assessment



No assessment information is available yet.

No assignments have been set for this course.

Recorded Lectures


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