{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# hw4 - Homework 4 Foundations of Computational Math 1 Fall...

This preview shows pages 1–2. Sign up to view the full content.

Homework 4 Foundations of Computational Math 1 Fall 2010 The solutions will be posted on Wednesday, 9/27/10 Problem 4.1 Recall that an elementary reflector has the form Q = I + αxx T R n × n with x 2 = 0. 4.1.a . Show that Q is orthogonal if and only if α = - 2 x T x or α = 0 4.1.b . Given v R n , let γ = ± v and x = v + γe 1 . Assuming that x = v show that x T x x T v = 2 4.1.c . Using the definitions and results above show that Qv = - γe 1 Problem 4.2 4.2.a This part of the problem concerns the computational complexity question of operation count. For both LU factorization and Householder reflector-based orthogonal factorization, we have used elementary transformations, T i , that can be characterized as rank-1 updates to the identity matrix, i.e., T i = I + x i y T i , x i R n and y i R n Gauss transforms and Householder reflectors differ in the definitions of the vectors x i and y i . Maintaining computational efficiency in terms of a reasonable operation count usually

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### 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