Terry D. Johnson
10.001 Fall 2000
In the problem below, we have order of magnitude differences
between coefficients in the different rows.
Step 0a: Find the entry in the left column with the largest absolute value. This entry is called the pivot.
Step 0b: Perform row interchange (if necessary), so that
the pivot is in the first row.
Step 1: Gaussian Elimination
Step 2: Find new pivot
Step 3: Switch rows (if necessary)
Step 4: Gaussian Elimination
Step 5: Find new pivot
Step 6: Switch rows (if necessary)
Step 7: Gaussian Elimination
Step 8: Back Substitute
-0.2x4 = -0.05; x4 = 4
100x3 + 200x4 = 800; x3 = 0
x2 + 2x3 + x4 =4; x2 = 0
x1 + 2x2 + x3 = 1;
x1 = 1
Pivoting helps reduce rounding errors; you are less likely to add/subtract with very small number (or very large) numbers.