d Form an approximation to A by truncating the last q terms in the singular

D form an approximation to a by truncating the last q

This preview shows page 2 - 3 out of 3 pages.

(d) Form an approximation to A by truncating the last q terms in the singular value de- composition: A 0 = R - q X k =1 σ k u k v T k . Apply the new pseudo-inverse A 0† to yn and plot the result. Try a number of different values of q , and choose the one which “looks best” to turn in (indicate the value of q used). Calculate the mean-square reconstruction error. (e) Now form another approximate inverse using Tikhonov regularization. Try a number of different values for δ and choose the one which “looks best” to turn in (indicate the value of δ used). Calculate the mean-square reconstruction error. (f) Summarize your findings by comparing the MSE in parts (c), (d), and (e). Also include the error of doing nothing: k x - yn 0 k 2 2 where yn 0 is the appropriate piece of yn . 2 Last updated 14:22, November 7, 2019
Image of page 2

Subscribe to view the full document.

4. Let A = 1 . 01 0 . 99 0 . 99 0 . 98 (a) Find the eigenvalue decomposition of A . Recall that λ is an eigenvalue of A if for some u [1] , u [2] (entries of the corresponding eigenvector) we have (1 . 01 - λ ) u [1] + 0 . 99 u [2] = 0 . 99 u [1] + (0 . 98 - λ ) u [2] = 0 . Another way of saying this is that we want the values of λ such that A - λ I (where I is the 2 × 2 identity matrix) has a non-trivial null space — there is a nonzero vector u such that ( A - λ I ) u = 0. Yet another way of saying this is that we want the values of λ such that det( A - λ I ) = 0. Once you have found the two eigenvalues, you can solve the 2 × 2 systems of equations Au 1 = λ 1 u 1 and Au 2 = λ 2 u 2 for u 1 and u 2 . (b) If y = 1 1 T , determine the solution to Ax = y .
Image of page 3
  • Fall '08
  • Staff

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern

Ask Expert Tutors You can ask You can ask ( soon) You can ask (will expire )
Answers in as fast as 15 minutes