Homework 8

Background: Ch. 34.1, 34.5, 34.3, 34.4, 31.1, 31.4.

Due November 11th:

• 8.1: CLR Exercise 34.1-1 (pg. 856).
• 8.2: CLR Exercise 34.4-1 (pg. 875).
• 8.3: CLR Exercise 31.4-4 (pg. 761)
• 8.4: CLR Problem 31-2 a,b,c (pg. 773)
  Hint: To compute the inverse of A, solve the linear system, Ax=b, n times, using a column of the identity matrix for b at each time. You only need to do LU-factorization once.
• 8.5: Prove the correctness and count the number of operations of the PLU-factorization algorithm.
  Hint: similar to the analysis of the LU-factorization algorithm