Partial Pivoting in Gaussian Elimination

Your computer is secretly terrible at algebra unless you force it to cheat.

When you are solving massive linear systems using Gaussian elimination, you are basically turning a complex

matrix into two simpler triangles called L and U. But here is the catch.

If the computer hits a zero or even a tiny number in the pivot spot, the whole calculation

crashes or gives you garbage answers due to rounding errors. The fix is called

partial pivoting. You literally swap the rows to put the biggest numbers on top.

It stops the math from breaking and keeps your code from exploding.