Iterative Improvement

For large sets of linear equations Ax = b, roundoff error may become a problem.
We want to know x but we only have x + x, which is an exact solution to A(x + x) = b + b.
Subtract the exact solution and eliminate b:
- Ax = A(x + x) - b
The RHS is known, hence can solve for x. Subtract this from the wrong solution to get an improved solution (make sure to use doubles!).

For large sets of linear equations Ax = b, roundoff error may become a problem.