  Gaussian elimination (GE) is the archetypal direct algorithm for solving
linear systems of equations and this has been its primary application for
thousands of years. In the last decade, GE has found another major use as an
iterative algorithm for low rank approximation. In this setting, GE is often
employed with complete pivoting and designed to allow for non-optimal pivoting,
i.e., pivoting mistakes, that could render GE numerically unstable when
implemented in floating point arithmetic. While it may appear that pivoting
mistakes could accumulate and lead to a large growth factor, we show that later
GE steps correct earlier pivoting mistakes, even while more are being made. In
short, GE is very robust to non-optimal pivots, allowing for its iterative
variant to flourish.
