{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# HW4 - compute the condition number by hand However you are...

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

EMAE 250.100: Homework 4 February 3, 2011 1. In some problems, it is possible to obtain a complex systems of equations (Text pp. 267), such that C ~x = ~ y, (1) where C M n × n is a matrix containing complex numbers. In this case, each term can be divided into the real number and the complex number terms, such that C = A + i B , ~x = ~a + i ~ b and ~ y = ~ c + i ~ d where A , B R n × n and ~ c, ~ d R n × 1 . Then, Eq. (1) can be rewritten by { A + i B } ( ~a + i ~ b ) = ( ~ c + i ~ d ) . (2) (a) [1pt] Using Eq. (2), show that A - B B A ! ~a ~ b ! = ~ c ~ d ! . (b) [2pt] Find ~x = ( x 1 , x 2 ) T using (a). 3 + 2 i 4 - i 1 ! x 1 x 2 ! = 2 + i 3 ! . 2. Given the following matrix A = 2 - 1 1 - 2 2 1 4 - 1 2 (a) [1pt] Derive an LU decomposition of A . (b) [2pt] Compute A - 1 by using the fact that A - 1 A = I and A = LU . 1

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

View Full Document
3. Compute the condition number for the following matrix and determine whether it is ‘ill-conditioned’, ‘well-conditioned’ or ‘perfectly conditioned’. Use one of matrix norms discussed in the lecture (clearly specify which one is used). You can use a calculator or MATLAB to compute the inverse of each matrix, but
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: compute the condition number by hand. However, you are still allowed to use a calculator for scalar multiplications. (a) [1pt] Find the condition number of the following matrix: A = 1 1 1 . 01-1-. 99-1-1 . (b) [1pt] Given A ~x = ~ b ﬁnd ~x = [ x 1 ,x 2 ,x 3 ] T where: i) ~ b = [1 ,-1 , 1] T and ii) ~ b = [1 . 01 ,-. 99 , 1 . 01] T and discuss your results in relation to the condition number computed in (a). (c) [1pt] Find the condition number of the following matrix: A = 3-2 1-1 4 1 2 5 3 . (d) [1pt] Given A ~x = ~ b ﬁnd ~x = [ x 1 ,x 2 ,x 3 ] T where: i) ~ b = [1 ,-1 , 1] T and ii) ~ b = [1 . 01 ,-. 99 , 1 . 01] T and discuss your results in relation to the condition number computed in (c). 2...
View Full 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