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School of Information Technology & Electrical Engineering

Engg7302 Advanced Computational Techniques in Engineering

Assignment 2: Numerical Linear Algebra

PART A                                             (This part is worth 16% of the total marks for the course)

Question 1

There is a signal b collected at M sampling points(b(1), b(2), …b(m), …,b(M)), and you are asked to strategically place N components x (x(1), x(2), …,x(n),…x(N)) into the system to   modify the signal profile. The modified signal profile is expressed as B=Ax+b.

The matrix A and vector b are stored in files: A.mat and b.mat, and in Matlab, you can access

the data as follows: load A; load b.

You are asked to implement the following task:

Figure 1: Illustration of the relationship between signals x, b and B.

The signal B will satisfy the following condition:

   ≤∈, where, Bo is the mean value of B.

And ∈ (m) = 0.0001, m=1,2,…M. In addition, b and B are both positive vectors. The range of components x: |x(n) | ≤ 0.01 , n=1,2, …,N.

You are asked to minimise the 1-norm of vector x.

Prepare the report on the solution details and prepare the Matlab code.

Note:  you are asked to use the functions fmincon() or linprog() in Matlab;

Task Description:

The student needs to prepare a report (at least three pages) on real-world applications that use concepts learned in the linear algebra (LA) part.

The presentation should contain the following sections

(1) introduction;

(2) theory/methods;

(3) results and discussion/interpretation;

(4) conclusion and

(5) reference.