CS3911 Reading List: Week 8

• Section 4.2.2 (This section will not be discussed in class; but, read it and verify the results anyway because the Cholesky method is important.)
• Polynomial interpolation and approximation slides file is in Inter-Approx.pdf.

• Problems P4.7, P4.11: Redo these problems with the iterative refinement method. More precisely, get the correct answer first, slightly change the correct answer a little, and apply the iterative refinement method a few iteration to improve the accuracy.
• 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.