There are lots of methods (e.g. LU) that are used millions of times a day, but don't have good error bounds. Most matrix algorithms used in practice have someth

There are lots of methods (e.g. LU) that are used millions of times a day, but don't have good error bounds. Most matrix algorithms used in practice have something resembling a proof of error bounds that everyone ignores because they don't do a good job of describing the error that you actually get when you use the methods.