midtermtwo174W09

midtermtwo174W09 - guess ~x = [1 , 1 , 1 , 1 , 1] t . 3 3....

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 174/274 Midterm 2 February 25, 2009 Please put your name, ID number, and sign and date. There are 4 problems worth a total of 100 points. Calculators are allowed but you must show your work to receive credit . Print Name: Student ID: Signature and Date: Problem Score 1 /25 2 /25 3 /25 4 /25 Total /100 1
Background image of page 1

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

View Full DocumentRight Arrow Icon
1. (25 pts) (a) Use Gaussian elimination with row pivoting to find the PLU factorization for the matrix A = 1 - 4 3 0 2 1 2 0 2 . (b) Explain how you can directly use the PLU factorization to solve the linear system A~x = ~ b in a fast way. 2
Background image of page 2
2. (25 pts) Consider the linear system A~x = ~ b with A = 2 0 0 0 - 1 0 - 2 0 - 1 0 - 2 0 4 0 1 0 0 0 - 1 0 0 2 0 0 3 . and b = [1 , 0 , - 1 , 0 , 2] t . Perform one iteration of Gauss-Seidel method using initial
Background image of page 3

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

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: guess ~x = [1 , 1 , 1 , 1 , 1] t . 3 3. (25 pts) Consider A~x = ~ b where A = a b c d . (a) Find conditions on bc/ad such that Jacobi method will converge for any initial guess. (b) Find conditions on bc/ad such that Gauss-Seidel method will converge for any initial guess. 4 4. (25 pts) Let p ( x ) be the polynomial of least degree interpolating the data points x-1 1-2 y 6 1 2 17 (a) Write out the Lagrange form for p ( x ). (b) Write out the Newton form for p ( x ). 5...
View Full Document

Page1 / 5

midtermtwo174W09 - guess ~x = [1 , 1 , 1 , 1 , 1] t . 3 3....

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online