When using Gauss-Jordan elimination to convert a matrix to an upper triangular matrix, truncation errors can drastically change the answer.
For example, when performing row operations with excel, with the following matrix:
Is reduced to:
The value in the red cell is a truncation error and should be zero. The next step in the algorithm would be to divide the 2nd last row by a constant to make the red cell equal to 1. If no truncation errors had occurred then this cell would have a value of zero. This drastically changes the final matrix. How could I correct for this?