Mini-Project

Deadline: Project Report should be submitted on Blackboard as a Word document or Adobe PDF by 6pm on Monday, 15 January 2018.

Summary

The aim of the mini-project is to investigate a topic in Scientific Computing which is related, but not covered in this module. It will require you to demonstrate

0 your ability to investigate a new topic through independent research, using resources available on the internet and/or in the library,

0 understanding of the researched material,

0 implementation of the described methods in Matlab,

0 use of the implemented methods on test examples,

0 your ability to present the studied topic and your computations in a written Project Report.

Project Report

The report should be about 5-8 pages long, written in Word or Latex. Equations should be properly formatted (use Insert Equation in Word) and cross-referenced, if necessary. The Report should be submitted in a single file (Word document or Adobe PDF).

The Report should contain the following sections:

Introduction : Here you should briefly discuss the background of the method (not more than 1 page), that is, what scientific computing problem(s) it solves.

Description of the algorithm: Here you should present the algorithm(s) behind the method. Give sufficient details to demonstrate your understanding of the structure of the algorithm(s).

Implementation : Discuss Matlab implementation of the algorithm(s), providing the Matlab code and explaining what different parts of the code do (relate to the description of the algorithm in the previous section).

Application : Give example(s) of the application of the algorithm to simple test problems. All numerical examples and results should be accompanied by the Matlab code that generated them.

Bibliography : Here you should list all the resources you've used in the preparation of the Report. All the items in the Bibliography list should be referenced in the text to indicate where in the Report they were used.

Mini-Project topics

1. Methods for computing eigenvalues and eigenvectors of a matrix (dflr1, jz224)

2. Conjugate gradient method (aak34, xm38)

3. QR factorisation of a matrix (zs119, sk711)

4. Singular Value Decomposition and Principal Component Analysis (anr8, jv97)

5. Broyden’s method for solving systems of nonlinear equations (gv44, hs267)

6. Hermite cubic interpolation (jtt9, zz154, jl580)

7. B-spline interpolation (sw487, yw367)

9. Multistep methods for solving ordinary differential equations (gf99, lsh25)

10. Shooting method for boundary value problem (jv97, zw119)

Note: Each topic is assigned to two students. It is OK for you to work together in researching the topic, learning about it, and deciding what test example(s) you are going to present. However, you should work independently when writing the Report and programming your Matlab code.

Mini-Project Consultations

When: Monday, 27 November

Where: 108 College House

Consultation on project topics (see the list above) will take place during the following times:

1. 10:00 – 10:20

2. 10:20 – 10:40

3. 10:40 – 11:00

4. 12:00 – 12:20

5. 12:20 – 12:40

6. 12:40 – 13:00

7. 15:00 – 15:20

8. 15:20 – 15:40

9. 15:40 – 16:00

10. 16:00 – 16:20

Preparation: Before attending the consultation meeting, you need to conduct the literature search (internet and/or library) and prepare a list of sources that you will use for your project. You will need to e-mail me this list before the meeting. During the meeting, we will review your list and discuss which sources are appropriate for your project. I can then make suggestions as to the plan for your project report.