CPSC/MATH 402: Algorithms for Solving Systems of Linear Equations
Due: Tuesday, March 9, 2004

Consider the following system of equations:

        2.51x + 1.48y + 4.53z = 0.05
        1.48x + 0.93y - 1.30z = 1.03
        2.68x + 3.04y - 1.48z = -0.53
  1. Solve the system using Gaussian elimination with naive pivoting (that is, no pivoting) and 3-digit arithmetic (round to nearest). In the process of solving find the L and U for the LU decomposition of the coefficient matrix.

  2. Compute the residual for your solution. What does the residual tell you? Does it give any helpful information about whether your solution is good or bad?

  3. Find the condition number for the coefficient matrix. What does it tell you about the system? Does it help you interpret your solution?

  4. Solve the system using Gaussian elimination with partial pivoting (3-digit arithmetic). Again find the L and U as you solve.

  5. Assess your solution from partial pivoting. Did partial pivoting help?

  6. Solve the system using scaled partial pivoting. (You may use the full precision of your calculator if you wish or you can stick to 3-digit arithmetic.)