CS3911 Reading List: Week 9

• Section 8.1: Pay special attention to the application examples, especially Section 8.1.1 as this section will be covered in Exam 2.

• Problems P8.1, P8.7, P8.9
• Do the following extra problems:
• Consider the following system of linear equations.
  • Use Jacobi's method to solve the following system of linear equations:
    
  • Do the same with Gauss-Seidel method.
  • Suppose a program delivered an inaccurate solution of x = 1.1, y = -0.8 and z = 1.4. Use iterative refinement to make this solution correct. The LU-decomposition of matrix A is shown below:
    
  • What is the determinant and rank of the following matrix. Use complete pivoting to solve this problem.
    
  • Is the following matrix diagonal dominant? Explain and elaborate your answer.
    
  • Find the inverse of the following matrix using the given LU-decomposition:
    

You do not have to turn in your paper. What I really expect you to do is using these problems to gauge your understanding of the subject. So, do the problems after finish reading the above sections.