EEL6502: HW2

Due Monday February 5 in class at 3pm. Late homework will not be accepted. Anytime you use Matlab (or similar program) you should hand in all of the files you used to generate your answers.

1. Do problems 4 and 5 in Chapter 4 in Widrow & Stearns.

   The rest of this assignment deals with searching the 2D performance surface for problem shown in Figure 2.6 in the book. We will use N=4.9626 throughout.

   Do the following parts without using Matlab:

2. Compute numerical values for R, p and .
3. Derive numerical values for the eigenvalues and eigenvectors of R.
4. Write R in normal form (i.e. diagonalized form) using the eigenvalues and eigenvectors in question 3.
5. Choose a value of the step size parameter for which for gradient descent search is overdamped for both dimensions. Call this value .
6. Choose a value of the step size parameter for which for gradient descent search is underdamped for both dimensions. Call this value .
7. Derive the optimal value of as discussed in class. Call this value .

   Do the following parts using Matlab.

8. Create data vectors 1000 elements long for and . If you have questions on how to create these vectors, you can refer to the file hw2_dat.mat in the course ftp directory.
9. Use the functions you wrote from hw1 and verify that the computed R, p and correspond to the analytic values derived in question 3.
10. Implement the simple gradient descent search using the known form of the gradient. Iterate the solution until a suitable MSE value is reached. Plot the MSE vs. iteration number on a linear plot for all three values of mu.
11. Use Matlab to create a contour plot showing several ellipses of constant MSE.
12. On the contour plot, show the convergence of the gradient descent procedure using each value of . The plot should resemble that shown in Figure 4.7 in the book.
13. Plot the MSE vs. iteration number on a semilogy plot for each case. Does the measured slope near zero MSE correspond to the value you expect in each case? Explain.