The optimised signal \( \mathbf{b}^{\prime} \) will satisfy the following condition:
\( \left|b^{\prime}-b 0\right| \leq \in \) b0, where, b0 is the mean value of \( b^{\prime} \).
And \( \in(m)=0.0008 \%, m=1,2, \ldots, M=576 \).
Additionally, both \( \mathbf{b} \) and \( \mathbf{b} \) ' are positive vectors.
For each component in vector \( \mathbf{x} \), the following conditions are required:
\[
0 \leq x(n)+x 0(n) \leq 0.007, n=1,2, \ldots, N=528
\]
Where vector \( \mathbf{x} \mathbf{0} \) has the same dimension as vector \( \mathbf{x} \) and represents pre-loaded components within the mesh structure depicted in Figure 1(b), indicating that not all meshes are empty before optimisation.
Matrix \( \mathbf{A} \), vectors \( \mathbf{b} \) and \( \mathbf{x} 0 \) are stored in the files A.mat, b.mat and \( \mathbf{x 0} \) mat respectively. You can access this data in MATLAB using the following commands: load \( A \); load \( b \); load \( x 0 \).
You are asked to minimise the 1-norm and 2-norm of vector \( \mathbf{x} \).
Please prepare the report on the solution details and develop the corresponding MATLAB code.
Note:
To minimise the 1-norm of vector \( \mathbf{x} \), use the function linprog ().
To minimise the 2 -norm of vector \( \mathbf{x} \), use the function fmincon ().
Question 2
(This question is worth \( 8 \% \) of the total marks for the course)
Assessment Type: Application
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 part.
The presentation should contain the following sections
(1) introduction;
(2) theory/methods;
(3) results and discussion/interpretation;
(4) conclusion and
(5) reference.
2
