ABSTRACT
As an example, consider the second part of Example 1.10. The order vector has the initial value or = [1 2 3]. After scaling, rows 1 and 3 are to be interchanged. Instead of actually interchanging these rows as done in Example 1.10, the corresponding elements of the order vector are changed to yield or = [3 2 I]. The first elimination step then uses the third row to eliminate Xl from the second and first rows. Pivoting is not required for the second elimination step, so the order vector is unchanged, and the second row is used to eliminate Xz from the first row. Back substitution is then performed in the reverse order of the order vector, 0, that is, in the order 1, 2, 3. This procedure saves computer time for large systems of equations, but at the expense of a slightly more complicated program.
