Pivoting: Why PLU Swaps Rows
An interactive live film: a 2 x 2 system with a tiny pivot solved for real in single precision; without the row swap the huge multiplier wipes out digits and the answer leaves the crossing of the two walls. Break it, then repair it.
Narration
Two equations in two unknowns: epsilon x zero plus x one equals one, and x zero plus x one equals two. Each equation is a wall standing on the floor, and the solution is where the walls cross, close to one, one.
Elimination uses the top left entry as its pivot. Here that pivot is epsilon, tiny, so the multiplier is one over epsilon: enormous.
The rest of the narration is in the book's Companion.
