the resulting approximation for the first 16 faces when r 16 using plotFaces b

# The resulting approximation for the first 16 faces

• Homework Help
• 3

This preview shows page 1 - 3 out of 3 pages.

the resulting approximation for the first 16 faces when r = 16 (using plotFaces ). (b) Plot each of the basis vectors for the subspace identified in the previous part when r = 16 (again using plotFaces ). (c) How large does r need to be to ensure that the relative error between the original dataset and our approximation is less than 5%? How does this relate to the singular values of the original matrix? (d) Comment on the qualitative differences between the original dataset and the approxi- mation produced by PCA and how this changes as we vary r . 3. Let A be a tri-diagonal matrix: A = d 1 c 1 0 0 0 · · · 0 f 1 d 2 c 2 0 0 · · · 0 0 f 2 d 3 c 3 0 · · · 0 0 0 f 3 d 4 c 4 · · · 0 . . . . . . . . . . . . . . . . . . 0 0 · · · f N - 2 d N - 1 c N - 1 0 0 0 · · · f N - 1 d N 1 Last updated 0:19, November 14, 2019

Subscribe to view the full document.

(a) Argue that the LU factorization of A has the form A = * 0 0 0 · · · 0 * * 0 0 · · · 0 0 * * 0 · · · 0 0 0 * * · · · 0 . . . . . . . . . . . . 0 0 · · · * * * * 0 0 0 · · · 0 0 * * 0 0 · · · 0 0 0 * * 0 · · · 0 . . . . . . . . . 0 0 · · · * * 0 0 · · · 0 * , where * signifies a non-zero term. (b) Write down an algorithm that computes the LU factorization of A , meaning the { i } , { u i } , and { g i } below A = 1 0 0 0 · · · 0 1 1 0 0 · · · 0 0 2 1 0 · · · 0 0 0 3 1 · · · 0 . . . . . . . . . . . . 0 0 · · · N - 1 1 u 1 g 1 0 0 0 · · · 0 0 u 2 g 2 0 0 · · · 0 0 0 u 3 g 3 0 · · · 0 .
• Fall '08
• Staff

### What students are saying

• 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.

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

• 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.

Dana University of Pennsylvania ‘17, Course Hero Intern

• 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.

Jill Tulane University ‘16, Course Hero Intern