Wikipedia says: In numerical linear algebra, the Jacobi method is an algorithm for determining the solutions of a diagonally dominant system of linear equations.

They made a slower method 200 times faster, and from the article it sounds like it will now be the preferred method for some problems. It would be interesting to see how it compares to the algorithms it will displace.

Talking about problems that take days to solve on large parallel computers, it would be interesting to hear how many megawatt hours of electricity this could save in a year.

... for finite differences of elliptic equations on a large grid. But that's still interesting.