### 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

- 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.

- 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?

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

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

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

- 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.)